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Join the community, latest research, protograph-based batched network codes.

zhu-mingyang/bnc • 29 Aug 2024

Batched network codes (BNCs) are a low-complexity solution for communication through networks with packet loss.

Information Theory Information Theory

A compact neuromorphic system for ultra energy-efficient, on-device robot localization

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ESPARGOS: Phase-Coherent WiFi CSI Datasets for Wireless Sensing Research

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Information Theory Signal Processing Information Theory

Understanding Privacy Norms through Web Forms

Users (i) are asked to input specific personal information types, and (ii) know the specific context (i. e., on which website and for what purpose).

Cryptography and Security

TINA: Acceleration of Non-NN Signal Processing Algorithms Using NN Accelerators

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Performance

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siamilab/robomnist • 29 Aug 2024

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MigVega/SLAM2REF • 28 Aug 2024

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VoxInstruct: Expressive Human Instruction-to-Speech Generation with Unified Multilingual Codec Language Modelling

thuhcsi/voxinstruct • 28 Aug 2024

To enable the model to automatically extract the content of synthesized speech from raw text instructions, we introduce speech semantic tokens as an intermediate representation for instruction-to-content guidance.

Sound Audio and Speech Processing

Order-preserving pattern mining with forgetting mechanism

wuc567/pattern-mining • 28 Aug 2024

Order-preserving pattern (OPP) mining is a type of sequential pattern mining method in which a group of ranks of time series is used to represent an OPP.

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Machine Learning: Algorithms, Real-World Applications and Research Directions

• Review Article
• Published: 22 March 2021
• Volume 2 , article number  160 , ( 2021 )

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• Iqbal H. Sarker   ORCID: orcid.org/0000-0003-1740-5517 1 , 2  

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In the current age of the Fourth Industrial Revolution (4 IR or Industry 4.0), the digital world has a wealth of data, such as Internet of Things (IoT) data, cybersecurity data, mobile data, business data, social media data, health data, etc. To intelligently analyze these data and develop the corresponding smart and automated  applications, the knowledge of artificial intelligence (AI), particularly, machine learning (ML) is the key. Various types of machine learning algorithms such as supervised, unsupervised, semi-supervised, and reinforcement learning exist in the area. Besides, the deep learning , which is part of a broader family of machine learning methods, can intelligently analyze the data on a large scale. In this paper, we present a comprehensive view on these machine learning algorithms that can be applied to enhance the intelligence and the capabilities of an application. Thus, this study’s key contribution is explaining the principles of different machine learning techniques and their applicability in various real-world application domains, such as cybersecurity systems, smart cities, healthcare, e-commerce, agriculture, and many more. We also highlight the challenges and potential research directions based on our study. Overall, this paper aims to serve as a reference point for both academia and industry professionals as well as for decision-makers in various real-world situations and application areas, particularly from the technical point of view.

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Introduction

We live in the age of data, where everything around us is connected to a data source, and everything in our lives is digitally recorded [ 21 , 103 ]. For instance, the current electronic world has a wealth of various kinds of data, such as the Internet of Things (IoT) data, cybersecurity data, smart city data, business data, smartphone data, social media data, health data, COVID-19 data, and many more. The data can be structured, semi-structured, or unstructured, discussed briefly in Sect. “ Types of Real-World Data and Machine Learning Techniques ”, which is increasing day-by-day. Extracting insights from these data can be used to build various intelligent applications in the relevant domains. For instance, to build a data-driven automated and intelligent cybersecurity system, the relevant cybersecurity data can be used [ 105 ]; to build personalized context-aware smart mobile applications, the relevant mobile data can be used [ 103 ], and so on. Thus, the data management tools and techniques having the capability of extracting insights or useful knowledge from the data in a timely and intelligent way is urgently needed, on which the real-world applications are based.

The worldwide popularity score of various types of ML algorithms (supervised, unsupervised, semi-supervised, and reinforcement) in a range of 0 (min) to 100 (max) over time where x-axis represents the timestamp information and y-axis represents the corresponding score

Artificial intelligence (AI), particularly, machine learning (ML) have grown rapidly in recent years in the context of data analysis and computing that typically allows the applications to function in an intelligent manner [ 95 ]. ML usually provides systems with the ability to learn and enhance from experience automatically without being specifically programmed and is generally referred to as the most popular latest technologies in the fourth industrial revolution (4 IR or Industry 4.0) [ 103 , 105 ]. “Industry 4.0” [ 114 ] is typically the ongoing automation of conventional manufacturing and industrial practices, including exploratory data processing, using new smart technologies such as machine learning automation. Thus, to intelligently analyze these data and to develop the corresponding real-world applications, machine learning algorithms is the key. The learning algorithms can be categorized into four major types, such as supervised, unsupervised, semi-supervised, and reinforcement learning in the area [ 75 ], discussed briefly in Sect. “ Types of Real-World Data and Machine Learning Techniques ”. The popularity of these approaches to learning is increasing day-by-day, which is shown in Fig. 1 , based on data collected from Google Trends [ 4 ] over the last five years. The x - axis of the figure indicates the specific dates and the corresponding popularity score within the range of \(0 \; (minimum)\) to \(100 \; (maximum)\) has been shown in y - axis . According to Fig. 1 , the popularity indication values for these learning types are low in 2015 and are increasing day by day. These statistics motivate us to study on machine learning in this paper, which can play an important role in the real-world through Industry 4.0 automation.

In general, the effectiveness and the efficiency of a machine learning solution depend on the nature and characteristics of data and the performance of the learning algorithms . In the area of machine learning algorithms, classification analysis, regression, data clustering, feature engineering and dimensionality reduction, association rule learning, or reinforcement learning techniques exist to effectively build data-driven systems [ 41 , 125 ]. Besides, deep learning originated from the artificial neural network that can be used to intelligently analyze data, which is known as part of a wider family of machine learning approaches [ 96 ]. Thus, selecting a proper learning algorithm that is suitable for the target application in a particular domain is challenging. The reason is that the purpose of different learning algorithms is different, even the outcome of different learning algorithms in a similar category may vary depending on the data characteristics [ 106 ]. Thus, it is important to understand the principles of various machine learning algorithms and their applicability to apply in various real-world application areas, such as IoT systems, cybersecurity services, business and recommendation systems, smart cities, healthcare and COVID-19, context-aware systems, sustainable agriculture, and many more that are explained briefly in Sect. “ Applications of Machine Learning ”.

Based on the importance and potentiality of “Machine Learning” to analyze the data mentioned above, in this paper, we provide a comprehensive view on various types of machine learning algorithms that can be applied to enhance the intelligence and the capabilities of an application. Thus, the key contribution of this study is explaining the principles and potentiality of different machine learning techniques, and their applicability in various real-world application areas mentioned earlier. The purpose of this paper is, therefore, to provide a basic guide for those academia and industry people who want to study, research, and develop data-driven automated and intelligent systems in the relevant areas based on machine learning techniques.

The key contributions of this paper are listed as follows:

To define the scope of our study by taking into account the nature and characteristics of various types of real-world data and the capabilities of various learning techniques.

To provide a comprehensive view on machine learning algorithms that can be applied to enhance the intelligence and capabilities of a data-driven application.

To discuss the applicability of machine learning-based solutions in various real-world application domains.

To highlight and summarize the potential research directions within the scope of our study for intelligent data analysis and services.

The rest of the paper is organized as follows. The next section presents the types of data and machine learning algorithms in a broader sense and defines the scope of our study. We briefly discuss and explain different machine learning algorithms in the subsequent section followed by which various real-world application areas based on machine learning algorithms are discussed and summarized. In the penultimate section, we highlight several research issues and potential future directions, and the final section concludes this paper.

Types of Real-World Data and Machine Learning Techniques

Machine learning algorithms typically consume and process data to learn the related patterns about individuals, business processes, transactions, events, and so on. In the following, we discuss various types of real-world data as well as categories of machine learning algorithms.

Types of Real-World Data

Usually, the availability of data is considered as the key to construct a machine learning model or data-driven real-world systems [ 103 , 105 ]. Data can be of various forms, such as structured, semi-structured, or unstructured [ 41 , 72 ]. Besides, the “metadata” is another type that typically represents data about the data. In the following, we briefly discuss these types of data.

Structured: It has a well-defined structure, conforms to a data model following a standard order, which is highly organized and easily accessed, and used by an entity or a computer program. In well-defined schemes, such as relational databases, structured data are typically stored, i.e., in a tabular format. For instance, names, dates, addresses, credit card numbers, stock information, geolocation, etc. are examples of structured data.

Unstructured: On the other hand, there is no pre-defined format or organization for unstructured data, making it much more difficult to capture, process, and analyze, mostly containing text and multimedia material. For example, sensor data, emails, blog entries, wikis, and word processing documents, PDF files, audio files, videos, images, presentations, web pages, and many other types of business documents can be considered as unstructured data.

Semi-structured: Semi-structured data are not stored in a relational database like the structured data mentioned above, but it does have certain organizational properties that make it easier to analyze. HTML, XML, JSON documents, NoSQL databases, etc., are some examples of semi-structured data.

Metadata: It is not the normal form of data, but “data about data”. The primary difference between “data” and “metadata” is that data are simply the material that can classify, measure, or even document something relative to an organization’s data properties. On the other hand, metadata describes the relevant data information, giving it more significance for data users. A basic example of a document’s metadata might be the author, file size, date generated by the document, keywords to define the document, etc.

In the area of machine learning and data science, researchers use various widely used datasets for different purposes. These are, for example, cybersecurity datasets such as NSL-KDD [ 119 ], UNSW-NB15 [ 76 ], ISCX’12 [ 1 ], CIC-DDoS2019 [ 2 ], Bot-IoT [ 59 ], etc., smartphone datasets such as phone call logs [ 84 , 101 ], SMS Log [ 29 ], mobile application usages logs [ 137 ] [ 117 ], mobile phone notification logs [ 73 ] etc., IoT data [ 16 , 57 , 62 ], agriculture and e-commerce data [ 120 , 138 ], health data such as heart disease [ 92 ], diabetes mellitus [ 83 , 134 ], COVID-19 [ 43 , 74 ], etc., and many more in various application domains. The data can be in different types discussed above, which may vary from application to application in the real world. To analyze such data in a particular problem domain, and to extract the insights or useful knowledge from the data for building the real-world intelligent applications, different types of machine learning techniques can be used according to their learning capabilities, which is discussed in the following.

Types of Machine Learning Techniques

Machine Learning algorithms are mainly divided into four categories: Supervised learning, Unsupervised learning, Semi-supervised learning, and Reinforcement learning [ 75 ], as shown in Fig. 2 . In the following, we briefly discuss each type of learning technique with the scope of their applicability to solve real-world problems.

Various types of machine learning techniques

Supervised: Supervised learning is typically the task of machine learning to learn a function that maps an input to an output based on sample input-output pairs [ 41 ]. It uses labeled training data and a collection of training examples to infer a function. Supervised learning is carried out when certain goals are identified to be accomplished from a certain set of inputs [ 105 ], i.e., a task-driven approach . The most common supervised tasks are “classification” that separates the data, and “regression” that fits the data. For instance, predicting the class label or sentiment of a piece of text, like a tweet or a product review, i.e., text classification, is an example of supervised learning.

Unsupervised: Unsupervised learning analyzes unlabeled datasets without the need for human interference, i.e., a data-driven process [ 41 ]. This is widely used for extracting generative features, identifying meaningful trends and structures, groupings in results, and exploratory purposes. The most common unsupervised learning tasks are clustering, density estimation, feature learning, dimensionality reduction, finding association rules, anomaly detection, etc.

Semi-supervised: Semi-supervised learning can be defined as a hybridization of the above-mentioned supervised and unsupervised methods, as it operates on both labeled and unlabeled data [ 41 , 105 ]. Thus, it falls between learning “without supervision” and learning “with supervision”. In the real world, labeled data could be rare in several contexts, and unlabeled data are numerous, where semi-supervised learning is useful [ 75 ]. The ultimate goal of a semi-supervised learning model is to provide a better outcome for prediction than that produced using the labeled data alone from the model. Some application areas where semi-supervised learning is used include machine translation, fraud detection, labeling data and text classification.

Reinforcement: Reinforcement learning is a type of machine learning algorithm that enables software agents and machines to automatically evaluate the optimal behavior in a particular context or environment to improve its efficiency [ 52 ], i.e., an environment-driven approach . This type of learning is based on reward or penalty, and its ultimate goal is to use insights obtained from environmental activists to take action to increase the reward or minimize the risk [ 75 ]. It is a powerful tool for training AI models that can help increase automation or optimize the operational efficiency of sophisticated systems such as robotics, autonomous driving tasks, manufacturing and supply chain logistics, however, not preferable to use it for solving the basic or straightforward problems.

Thus, to build effective models in various application areas different types of machine learning techniques can play a significant role according to their learning capabilities, depending on the nature of the data discussed earlier, and the target outcome. In Table 1 , we summarize various types of machine learning techniques with examples. In the following, we provide a comprehensive view of machine learning algorithms that can be applied to enhance the intelligence and capabilities of a data-driven application.

Machine Learning Tasks and Algorithms

In this section, we discuss various machine learning algorithms that include classification analysis, regression analysis, data clustering, association rule learning, feature engineering for dimensionality reduction, as well as deep learning methods. A general structure of a machine learning-based predictive model has been shown in Fig. 3 , where the model is trained from historical data in phase 1 and the outcome is generated in phase 2 for the new test data.

A general structure of a machine learning based predictive model considering both the training and testing phase

Classification Analysis

Classification is regarded as a supervised learning method in machine learning, referring to a problem of predictive modeling as well, where a class label is predicted for a given example [ 41 ]. Mathematically, it maps a function ( f ) from input variables ( X ) to output variables ( Y ) as target, label or categories. To predict the class of given data points, it can be carried out on structured or unstructured data. For example, spam detection such as “spam” and “not spam” in email service providers can be a classification problem. In the following, we summarize the common classification problems.

Binary classification: It refers to the classification tasks having two class labels such as “true and false” or “yes and no” [ 41 ]. In such binary classification tasks, one class could be the normal state, while the abnormal state could be another class. For instance, “cancer not detected” is the normal state of a task that involves a medical test, and “cancer detected” could be considered as the abnormal state. Similarly, “spam” and “not spam” in the above example of email service providers are considered as binary classification.

Multiclass classification: Traditionally, this refers to those classification tasks having more than two class labels [ 41 ]. The multiclass classification does not have the principle of normal and abnormal outcomes, unlike binary classification tasks. Instead, within a range of specified classes, examples are classified as belonging to one. For example, it can be a multiclass classification task to classify various types of network attacks in the NSL-KDD [ 119 ] dataset, where the attack categories are classified into four class labels, such as DoS (Denial of Service Attack), U2R (User to Root Attack), R2L (Root to Local Attack), and Probing Attack.

Multi-label classification: In machine learning, multi-label classification is an important consideration where an example is associated with several classes or labels. Thus, it is a generalization of multiclass classification, where the classes involved in the problem are hierarchically structured, and each example may simultaneously belong to more than one class in each hierarchical level, e.g., multi-level text classification. For instance, Google news can be presented under the categories of a “city name”, “technology”, or “latest news”, etc. Multi-label classification includes advanced machine learning algorithms that support predicting various mutually non-exclusive classes or labels, unlike traditional classification tasks where class labels are mutually exclusive [ 82 ].

Many classification algorithms have been proposed in the machine learning and data science literature [ 41 , 125 ]. In the following, we summarize the most common and popular methods that are used widely in various application areas.

Naive Bayes (NB): The naive Bayes algorithm is based on the Bayes’ theorem with the assumption of independence between each pair of features [ 51 ]. It works well and can be used for both binary and multi-class categories in many real-world situations, such as document or text classification, spam filtering, etc. To effectively classify the noisy instances in the data and to construct a robust prediction model, the NB classifier can be used [ 94 ]. The key benefit is that, compared to more sophisticated approaches, it needs a small amount of training data to estimate the necessary parameters and quickly [ 82 ]. However, its performance may affect due to its strong assumptions on features independence. Gaussian, Multinomial, Complement, Bernoulli, and Categorical are the common variants of NB classifier [ 82 ].

Linear Discriminant Analysis (LDA): Linear Discriminant Analysis (LDA) is a linear decision boundary classifier created by fitting class conditional densities to data and applying Bayes’ rule [ 51 , 82 ]. This method is also known as a generalization of Fisher’s linear discriminant, which projects a given dataset into a lower-dimensional space, i.e., a reduction of dimensionality that minimizes the complexity of the model or reduces the resulting model’s computational costs. The standard LDA model usually suits each class with a Gaussian density, assuming that all classes share the same covariance matrix [ 82 ]. LDA is closely related to ANOVA (analysis of variance) and regression analysis, which seek to express one dependent variable as a linear combination of other features or measurements.

Logistic regression (LR): Another common probabilistic based statistical model used to solve classification issues in machine learning is Logistic Regression (LR) [ 64 ]. Logistic regression typically uses a logistic function to estimate the probabilities, which is also referred to as the mathematically defined sigmoid function in Eq. 1 . It can overfit high-dimensional datasets and works well when the dataset can be separated linearly. The regularization (L1 and L2) techniques [ 82 ] can be used to avoid over-fitting in such scenarios. The assumption of linearity between the dependent and independent variables is considered as a major drawback of Logistic Regression. It can be used for both classification and regression problems, but it is more commonly used for classification.

K-nearest neighbors (KNN): K-Nearest Neighbors (KNN) [ 9 ] is an “instance-based learning” or non-generalizing learning, also known as a “lazy learning” algorithm. It does not focus on constructing a general internal model; instead, it stores all instances corresponding to training data in n -dimensional space. KNN uses data and classifies new data points based on similarity measures (e.g., Euclidean distance function) [ 82 ]. Classification is computed from a simple majority vote of the k nearest neighbors of each point. It is quite robust to noisy training data, and accuracy depends on the data quality. The biggest issue with KNN is to choose the optimal number of neighbors to be considered. KNN can be used both for classification as well as regression.

Support vector machine (SVM): In machine learning, another common technique that can be used for classification, regression, or other tasks is a support vector machine (SVM) [ 56 ]. In high- or infinite-dimensional space, a support vector machine constructs a hyper-plane or set of hyper-planes. Intuitively, the hyper-plane, which has the greatest distance from the nearest training data points in any class, achieves a strong separation since, in general, the greater the margin, the lower the classifier’s generalization error. It is effective in high-dimensional spaces and can behave differently based on different mathematical functions known as the kernel. Linear, polynomial, radial basis function (RBF), sigmoid, etc., are the popular kernel functions used in SVM classifier [ 82 ]. However, when the data set contains more noise, such as overlapping target classes, SVM does not perform well.

Decision tree (DT): Decision tree (DT) [ 88 ] is a well-known non-parametric supervised learning method. DT learning methods are used for both the classification and regression tasks [ 82 ]. ID3 [ 87 ], C4.5 [ 88 ], and CART [ 20 ] are well known for DT algorithms. Moreover, recently proposed BehavDT [ 100 ], and IntrudTree [ 97 ] by Sarker et al. are effective in the relevant application domains, such as user behavior analytics and cybersecurity analytics, respectively. By sorting down the tree from the root to some leaf nodes, as shown in Fig. 4 , DT classifies the instances. Instances are classified by checking the attribute defined by that node, starting at the root node of the tree, and then moving down the tree branch corresponding to the attribute value. For splitting, the most popular criteria are “gini” for the Gini impurity and “entropy” for the information gain that can be expressed mathematically as [ 82 ].

An example of a decision tree structure

An example of a random forest structure considering multiple decision trees

Random forest (RF): A random forest classifier [ 19 ] is well known as an ensemble classification technique that is used in the field of machine learning and data science in various application areas. This method uses “parallel ensembling” which fits several decision tree classifiers in parallel, as shown in Fig. 5 , on different data set sub-samples and uses majority voting or averages for the outcome or final result. It thus minimizes the over-fitting problem and increases the prediction accuracy and control [ 82 ]. Therefore, the RF learning model with multiple decision trees is typically more accurate than a single decision tree based model [ 106 ]. To build a series of decision trees with controlled variation, it combines bootstrap aggregation (bagging) [ 18 ] and random feature selection [ 11 ]. It is adaptable to both classification and regression problems and fits well for both categorical and continuous values.

Adaptive Boosting (AdaBoost): Adaptive Boosting (AdaBoost) is an ensemble learning process that employs an iterative approach to improve poor classifiers by learning from their errors. This is developed by Yoav Freund et al. [ 35 ] and also known as “meta-learning”. Unlike the random forest that uses parallel ensembling, Adaboost uses “sequential ensembling”. It creates a powerful classifier by combining many poorly performing classifiers to obtain a good classifier of high accuracy. In that sense, AdaBoost is called an adaptive classifier by significantly improving the efficiency of the classifier, but in some instances, it can trigger overfits. AdaBoost is best used to boost the performance of decision trees, base estimator [ 82 ], on binary classification problems, however, is sensitive to noisy data and outliers.

Extreme gradient boosting (XGBoost): Gradient Boosting, like Random Forests [ 19 ] above, is an ensemble learning algorithm that generates a final model based on a series of individual models, typically decision trees. The gradient is used to minimize the loss function, similar to how neural networks [ 41 ] use gradient descent to optimize weights. Extreme Gradient Boosting (XGBoost) is a form of gradient boosting that takes more detailed approximations into account when determining the best model [ 82 ]. It computes second-order gradients of the loss function to minimize loss and advanced regularization (L1 and L2) [ 82 ], which reduces over-fitting, and improves model generalization and performance. XGBoost is fast to interpret and can handle large-sized datasets well.

Stochastic gradient descent (SGD): Stochastic gradient descent (SGD) [ 41 ] is an iterative method for optimizing an objective function with appropriate smoothness properties, where the word ‘stochastic’ refers to random probability. This reduces the computational burden, particularly in high-dimensional optimization problems, allowing for faster iterations in exchange for a lower convergence rate. A gradient is the slope of a function that calculates a variable’s degree of change in response to another variable’s changes. Mathematically, the Gradient Descent is a convex function whose output is a partial derivative of a set of its input parameters. Let, \(\alpha\) is the learning rate, and \(J_i\) is the training example cost of \(i \mathrm{th}\) , then Eq. ( 4 ) represents the stochastic gradient descent weight update method at the \(j^\mathrm{th}\) iteration. In large-scale and sparse machine learning, SGD has been successfully applied to problems often encountered in text classification and natural language processing [ 82 ]. However, SGD is sensitive to feature scaling and needs a range of hyperparameters, such as the regularization parameter and the number of iterations.

Rule-based classification : The term rule-based classification can be used to refer to any classification scheme that makes use of IF-THEN rules for class prediction. Several classification algorithms such as Zero-R [ 125 ], One-R [ 47 ], decision trees [ 87 , 88 ], DTNB [ 110 ], Ripple Down Rule learner (RIDOR) [ 125 ], Repeated Incremental Pruning to Produce Error Reduction (RIPPER) [ 126 ] exist with the ability of rule generation. The decision tree is one of the most common rule-based classification algorithms among these techniques because it has several advantages, such as being easier to interpret; the ability to handle high-dimensional data; simplicity and speed; good accuracy; and the capability to produce rules for human clear and understandable classification [ 127 ] [ 128 ]. The decision tree-based rules also provide significant accuracy in a prediction model for unseen test cases [ 106 ]. Since the rules are easily interpretable, these rule-based classifiers are often used to produce descriptive models that can describe a system including the entities and their relationships.

Classification vs. regression. In classification the dotted line represents a linear boundary that separates the two classes; in regression, the dotted line models the linear relationship between the two variables

Regression Analysis

Regression analysis includes several methods of machine learning that allow to predict a continuous ( y ) result variable based on the value of one or more ( x ) predictor variables [ 41 ]. The most significant distinction between classification and regression is that classification predicts distinct class labels, while regression facilitates the prediction of a continuous quantity. Figure 6 shows an example of how classification is different with regression models. Some overlaps are often found between the two types of machine learning algorithms. Regression models are now widely used in a variety of fields, including financial forecasting or prediction, cost estimation, trend analysis, marketing, time series estimation, drug response modeling, and many more. Some of the familiar types of regression algorithms are linear, polynomial, lasso and ridge regression, etc., which are explained briefly in the following.

Simple and multiple linear regression: This is one of the most popular ML modeling techniques as well as a well-known regression technique. In this technique, the dependent variable is continuous, the independent variable(s) can be continuous or discrete, and the form of the regression line is linear. Linear regression creates a relationship between the dependent variable ( Y ) and one or more independent variables ( X ) (also known as regression line) using the best fit straight line [ 41 ]. It is defined by the following equations:

where a is the intercept, b is the slope of the line, and e is the error term. This equation can be used to predict the value of the target variable based on the given predictor variable(s). Multiple linear regression is an extension of simple linear regression that allows two or more predictor variables to model a response variable, y, as a linear function [ 41 ] defined in Eq. 6 , whereas simple linear regression has only 1 independent variable, defined in Eq. 5 .

Polynomial regression: Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is not linear, but is the polynomial degree of \(n^\mathrm{th}\) in x [ 82 ]. The equation for polynomial regression is also derived from linear regression (polynomial regression of degree 1) equation, which is defined as below:

Here, y is the predicted/target output, \(b_0, b_1,... b_n\) are the regression coefficients, x is an independent/ input variable. In simple words, we can say that if data are not distributed linearly, instead it is \(n^\mathrm{th}\) degree of polynomial then we use polynomial regression to get desired output.

LASSO and ridge regression: LASSO and Ridge regression are well known as powerful techniques which are typically used for building learning models in presence of a large number of features, due to their capability to preventing over-fitting and reducing the complexity of the model. The LASSO (least absolute shrinkage and selection operator) regression model uses L 1 regularization technique [ 82 ] that uses shrinkage, which penalizes “absolute value of magnitude of coefficients” ( L 1 penalty). As a result, LASSO appears to render coefficients to absolute zero. Thus, LASSO regression aims to find the subset of predictors that minimizes the prediction error for a quantitative response variable. On the other hand, ridge regression uses L 2 regularization [ 82 ], which is the “squared magnitude of coefficients” ( L 2 penalty). Thus, ridge regression forces the weights to be small but never sets the coefficient value to zero, and does a non-sparse solution. Overall, LASSO regression is useful to obtain a subset of predictors by eliminating less important features, and ridge regression is useful when a data set has “multicollinearity” which refers to the predictors that are correlated with other predictors.

Cluster Analysis

Cluster analysis, also known as clustering, is an unsupervised machine learning technique for identifying and grouping related data points in large datasets without concern for the specific outcome. It does grouping a collection of objects in such a way that objects in the same category, called a cluster, are in some sense more similar to each other than objects in other groups [ 41 ]. It is often used as a data analysis technique to discover interesting trends or patterns in data, e.g., groups of consumers based on their behavior. In a broad range of application areas, such as cybersecurity, e-commerce, mobile data processing, health analytics, user modeling and behavioral analytics, clustering can be used. In the following, we briefly discuss and summarize various types of clustering methods.

Partitioning methods: Based on the features and similarities in the data, this clustering approach categorizes the data into multiple groups or clusters. The data scientists or analysts typically determine the number of clusters either dynamically or statically depending on the nature of the target applications, to produce for the methods of clustering. The most common clustering algorithms based on partitioning methods are K-means [ 69 ], K-Mediods [ 80 ], CLARA [ 55 ] etc.

Density-based methods: To identify distinct groups or clusters, it uses the concept that a cluster in the data space is a contiguous region of high point density isolated from other such clusters by contiguous regions of low point density. Points that are not part of a cluster are considered as noise. The typical clustering algorithms based on density are DBSCAN [ 32 ], OPTICS [ 12 ] etc. The density-based methods typically struggle with clusters of similar density and high dimensionality data.

Hierarchical-based methods: Hierarchical clustering typically seeks to construct a hierarchy of clusters, i.e., the tree structure. Strategies for hierarchical clustering generally fall into two types: (i) Agglomerative—a “bottom-up” approach in which each observation begins in its cluster and pairs of clusters are combined as one, moves up the hierarchy, and (ii) Divisive—a “top-down” approach in which all observations begin in one cluster and splits are performed recursively, moves down the hierarchy, as shown in Fig 7 . Our earlier proposed BOTS technique, Sarker et al. [ 102 ] is an example of a hierarchical, particularly, bottom-up clustering algorithm.

Grid-based methods: To deal with massive datasets, grid-based clustering is especially suitable. To obtain clusters, the principle is first to summarize the dataset with a grid representation and then to combine grid cells. STING [ 122 ], CLIQUE [ 6 ], etc. are the standard algorithms of grid-based clustering.

Model-based methods: There are mainly two types of model-based clustering algorithms: one that uses statistical learning, and the other based on a method of neural network learning [ 130 ]. For instance, GMM [ 89 ] is an example of a statistical learning method, and SOM [ 22 ] [ 96 ] is an example of a neural network learning method.

Constraint-based methods: Constrained-based clustering is a semi-supervised approach to data clustering that uses constraints to incorporate domain knowledge. Application or user-oriented constraints are incorporated to perform the clustering. The typical algorithms of this kind of clustering are COP K-means [ 121 ], CMWK-Means [ 27 ], etc.

A graphical interpretation of the widely-used hierarchical clustering (Bottom-up and top-down) technique

Many clustering algorithms have been proposed with the ability to grouping data in machine learning and data science literature [ 41 , 125 ]. In the following, we summarize the popular methods that are used widely in various application areas.

K-means clustering: K-means clustering [ 69 ] is a fast, robust, and simple algorithm that provides reliable results when data sets are well-separated from each other. The data points are allocated to a cluster in this algorithm in such a way that the amount of the squared distance between the data points and the centroid is as small as possible. In other words, the K-means algorithm identifies the k number of centroids and then assigns each data point to the nearest cluster while keeping the centroids as small as possible. Since it begins with a random selection of cluster centers, the results can be inconsistent. Since extreme values can easily affect a mean, the K-means clustering algorithm is sensitive to outliers. K-medoids clustering [ 91 ] is a variant of K-means that is more robust to noises and outliers.

Mean-shift clustering: Mean-shift clustering [ 37 ] is a nonparametric clustering technique that does not require prior knowledge of the number of clusters or constraints on cluster shape. Mean-shift clustering aims to discover “blobs” in a smooth distribution or density of samples [ 82 ]. It is a centroid-based algorithm that works by updating centroid candidates to be the mean of the points in a given region. To form the final set of centroids, these candidates are filtered in a post-processing stage to remove near-duplicates. Cluster analysis in computer vision and image processing are examples of application domains. Mean Shift has the disadvantage of being computationally expensive. Moreover, in cases of high dimension, where the number of clusters shifts abruptly, the mean-shift algorithm does not work well.

DBSCAN: Density-based spatial clustering of applications with noise (DBSCAN) [ 32 ] is a base algorithm for density-based clustering which is widely used in data mining and machine learning. This is known as a non-parametric density-based clustering technique for separating high-density clusters from low-density clusters that are used in model building. DBSCAN’s main idea is that a point belongs to a cluster if it is close to many points from that cluster. It can find clusters of various shapes and sizes in a vast volume of data that is noisy and contains outliers. DBSCAN, unlike k-means, does not require a priori specification of the number of clusters in the data and can find arbitrarily shaped clusters. Although k-means is much faster than DBSCAN, it is efficient at finding high-density regions and outliers, i.e., is robust to outliers.

GMM clustering: Gaussian mixture models (GMMs) are often used for data clustering, which is a distribution-based clustering algorithm. A Gaussian mixture model is a probabilistic model in which all the data points are produced by a mixture of a finite number of Gaussian distributions with unknown parameters [ 82 ]. To find the Gaussian parameters for each cluster, an optimization algorithm called expectation-maximization (EM) [ 82 ] can be used. EM is an iterative method that uses a statistical model to estimate the parameters. In contrast to k-means, Gaussian mixture models account for uncertainty and return the likelihood that a data point belongs to one of the k clusters. GMM clustering is more robust than k-means and works well even with non-linear data distributions.

Agglomerative hierarchical clustering: The most common method of hierarchical clustering used to group objects in clusters based on their similarity is agglomerative clustering. This technique uses a bottom-up approach, where each object is first treated as a singleton cluster by the algorithm. Following that, pairs of clusters are merged one by one until all clusters have been merged into a single large cluster containing all objects. The result is a dendrogram, which is a tree-based representation of the elements. Single linkage [ 115 ], Complete linkage [ 116 ], BOTS [ 102 ] etc. are some examples of such techniques. The main advantage of agglomerative hierarchical clustering over k-means is that the tree-structure hierarchy generated by agglomerative clustering is more informative than the unstructured collection of flat clusters returned by k-means, which can help to make better decisions in the relevant application areas.

Dimensionality Reduction and Feature Learning

In machine learning and data science, high-dimensional data processing is a challenging task for both researchers and application developers. Thus, dimensionality reduction which is an unsupervised learning technique, is important because it leads to better human interpretations, lower computational costs, and avoids overfitting and redundancy by simplifying models. Both the process of feature selection and feature extraction can be used for dimensionality reduction. The primary distinction between the selection and extraction of features is that the “feature selection” keeps a subset of the original features [ 97 ], while “feature extraction” creates brand new ones [ 98 ]. In the following, we briefly discuss these techniques.

Feature selection: The selection of features, also known as the selection of variables or attributes in the data, is the process of choosing a subset of unique features (variables, predictors) to use in building machine learning and data science model. It decreases a model’s complexity by eliminating the irrelevant or less important features and allows for faster training of machine learning algorithms. A right and optimal subset of the selected features in a problem domain is capable to minimize the overfitting problem through simplifying and generalizing the model as well as increases the model’s accuracy [ 97 ]. Thus, “feature selection” [ 66 , 99 ] is considered as one of the primary concepts in machine learning that greatly affects the effectiveness and efficiency of the target machine learning model. Chi-squared test, Analysis of variance (ANOVA) test, Pearson’s correlation coefficient, recursive feature elimination, are some popular techniques that can be used for feature selection.

Feature extraction: In a machine learning-based model or system, feature extraction techniques usually provide a better understanding of the data, a way to improve prediction accuracy, and to reduce computational cost or training time. The aim of “feature extraction” [ 66 , 99 ] is to reduce the number of features in a dataset by generating new ones from the existing ones and then discarding the original features. The majority of the information found in the original set of features can then be summarized using this new reduced set of features. For instance, principal components analysis (PCA) is often used as a dimensionality-reduction technique to extract a lower-dimensional space creating new brand components from the existing features in a dataset [ 98 ].

Many algorithms have been proposed to reduce data dimensions in the machine learning and data science literature [ 41 , 125 ]. In the following, we summarize the popular methods that are used widely in various application areas.

Variance threshold: A simple basic approach to feature selection is the variance threshold [ 82 ]. This excludes all features of low variance, i.e., all features whose variance does not exceed the threshold. It eliminates all zero-variance characteristics by default, i.e., characteristics that have the same value in all samples. This feature selection algorithm looks only at the ( X ) features, not the ( y ) outputs needed, and can, therefore, be used for unsupervised learning.

Pearson correlation: Pearson’s correlation is another method to understand a feature’s relation to the response variable and can be used for feature selection [ 99 ]. This method is also used for finding the association between the features in a dataset. The resulting value is \([-1, 1]\) , where \(-1\) means perfect negative correlation, \(+1\) means perfect positive correlation, and 0 means that the two variables do not have a linear correlation. If two random variables represent X and Y , then the correlation coefficient between X and Y is defined as [ 41 ]

ANOVA: Analysis of variance (ANOVA) is a statistical tool used to verify the mean values of two or more groups that differ significantly from each other. ANOVA assumes a linear relationship between the variables and the target and the variables’ normal distribution. To statistically test the equality of means, the ANOVA method utilizes F tests. For feature selection, the results ‘ANOVA F value’ [ 82 ] of this test can be used where certain features independent of the goal variable can be omitted.

Chi square: The chi-square \({\chi }^2\) [ 82 ] statistic is an estimate of the difference between the effects of a series of events or variables observed and expected frequencies. The magnitude of the difference between the real and observed values, the degrees of freedom, and the sample size depends on \({\chi }^2\) . The chi-square \({\chi }^2\) is commonly used for testing relationships between categorical variables. If \(O_i\) represents observed value and \(E_i\) represents expected value, then

Recursive feature elimination (RFE): Recursive Feature Elimination (RFE) is a brute force approach to feature selection. RFE [ 82 ] fits the model and removes the weakest feature before it meets the specified number of features. Features are ranked by the coefficients or feature significance of the model. RFE aims to remove dependencies and collinearity in the model by recursively removing a small number of features per iteration.

Model-based selection: To reduce the dimensionality of the data, linear models penalized with the L 1 regularization can be used. Least absolute shrinkage and selection operator (Lasso) regression is a type of linear regression that has the property of shrinking some of the coefficients to zero [ 82 ]. Therefore, that feature can be removed from the model. Thus, the penalized lasso regression method, often used in machine learning to select the subset of variables. Extra Trees Classifier [ 82 ] is an example of a tree-based estimator that can be used to compute impurity-based function importance, which can then be used to discard irrelevant features.

Principal component analysis (PCA): Principal component analysis (PCA) is a well-known unsupervised learning approach in the field of machine learning and data science. PCA is a mathematical technique that transforms a set of correlated variables into a set of uncorrelated variables known as principal components [ 48 , 81 ]. Figure 8 shows an example of the effect of PCA on various dimensions space, where Fig. 8 a shows the original features in 3D space, and Fig. 8 b shows the created principal components PC1 and PC2 onto a 2D plane, and 1D line with the principal component PC1 respectively. Thus, PCA can be used as a feature extraction technique that reduces the dimensionality of the datasets, and to build an effective machine learning model [ 98 ]. Technically, PCA identifies the completely transformed with the highest eigenvalues of a covariance matrix and then uses those to project the data into a new subspace of equal or fewer dimensions [ 82 ].

An example of a principal component analysis (PCA) and created principal components PC1 and PC2 in different dimension space

Association Rule Learning

Association rule learning is a rule-based machine learning approach to discover interesting relationships, “IF-THEN” statements, in large datasets between variables [ 7 ]. One example is that “if a customer buys a computer or laptop (an item), s/he is likely to also buy anti-virus software (another item) at the same time”. Association rules are employed today in many application areas, including IoT services, medical diagnosis, usage behavior analytics, web usage mining, smartphone applications, cybersecurity applications, and bioinformatics. In comparison to sequence mining, association rule learning does not usually take into account the order of things within or across transactions. A common way of measuring the usefulness of association rules is to use its parameter, the ‘support’ and ‘confidence’, which is introduced in [ 7 ].

In the data mining literature, many association rule learning methods have been proposed, such as logic dependent [ 34 ], frequent pattern based [ 8 , 49 , 68 ], and tree-based [ 42 ]. The most popular association rule learning algorithms are summarized below.

AIS and SETM: AIS is the first algorithm proposed by Agrawal et al. [ 7 ] for association rule mining. The AIS algorithm’s main downside is that too many candidate itemsets are generated, requiring more space and wasting a lot of effort. This algorithm calls for too many passes over the entire dataset to produce the rules. Another approach SETM [ 49 ] exhibits good performance and stable behavior with execution time; however, it suffers from the same flaw as the AIS algorithm.

Apriori: For generating association rules for a given dataset, Agrawal et al. [ 8 ] proposed the Apriori, Apriori-TID, and Apriori-Hybrid algorithms. These later algorithms outperform the AIS and SETM mentioned above due to the Apriori property of frequent itemset [ 8 ]. The term ‘Apriori’ usually refers to having prior knowledge of frequent itemset properties. Apriori uses a “bottom-up” approach, where it generates the candidate itemsets. To reduce the search space, Apriori uses the property “all subsets of a frequent itemset must be frequent; and if an itemset is infrequent, then all its supersets must also be infrequent”. Another approach predictive Apriori [ 108 ] can also generate rules; however, it receives unexpected results as it combines both the support and confidence. The Apriori [ 8 ] is the widely applicable techniques in mining association rules.

ECLAT: This technique was proposed by Zaki et al. [ 131 ] and stands for Equivalence Class Clustering and bottom-up Lattice Traversal. ECLAT uses a depth-first search to find frequent itemsets. In contrast to the Apriori [ 8 ] algorithm, which represents data in a horizontal pattern, it represents data vertically. Hence, the ECLAT algorithm is more efficient and scalable in the area of association rule learning. This algorithm is better suited for small and medium datasets whereas the Apriori algorithm is used for large datasets.

FP-Growth: Another common association rule learning technique based on the frequent-pattern tree (FP-tree) proposed by Han et al. [ 42 ] is Frequent Pattern Growth, known as FP-Growth. The key difference with Apriori is that while generating rules, the Apriori algorithm [ 8 ] generates frequent candidate itemsets; on the other hand, the FP-growth algorithm [ 42 ] prevents candidate generation and thus produces a tree by the successful strategy of ‘divide and conquer’ approach. Due to its sophistication, however, FP-Tree is challenging to use in an interactive mining environment [ 133 ]. Thus, the FP-Tree would not fit into memory for massive data sets, making it challenging to process big data as well. Another solution is RARM (Rapid Association Rule Mining) proposed by Das et al. [ 26 ] but faces a related FP-tree issue [ 133 ].

ABC-RuleMiner: A rule-based machine learning method, recently proposed in our earlier paper, by Sarker et al. [ 104 ], to discover the interesting non-redundant rules to provide real-world intelligent services. This algorithm effectively identifies the redundancy in associations by taking into account the impact or precedence of the related contextual features and discovers a set of non-redundant association rules. This algorithm first constructs an association generation tree (AGT), a top-down approach, and then extracts the association rules through traversing the tree. Thus, ABC-RuleMiner is more potent than traditional rule-based methods in terms of both non-redundant rule generation and intelligent decision-making, particularly in a context-aware smart computing environment, where human or user preferences are involved.

Among the association rule learning techniques discussed above, Apriori [ 8 ] is the most widely used algorithm for discovering association rules from a given dataset [ 133 ]. The main strength of the association learning technique is its comprehensiveness, as it generates all associations that satisfy the user-specified constraints, such as minimum support and confidence value. The ABC-RuleMiner approach [ 104 ] discussed earlier could give significant results in terms of non-redundant rule generation and intelligent decision-making for the relevant application areas in the real world.

Reinforcement Learning

Reinforcement learning (RL) is a machine learning technique that allows an agent to learn by trial and error in an interactive environment using input from its actions and experiences. Unlike supervised learning, which is based on given sample data or examples, the RL method is based on interacting with the environment. The problem to be solved in reinforcement learning (RL) is defined as a Markov Decision Process (MDP) [ 86 ], i.e., all about sequentially making decisions. An RL problem typically includes four elements such as Agent, Environment, Rewards, and Policy.

RL can be split roughly into Model-based and Model-free techniques. Model-based RL is the process of inferring optimal behavior from a model of the environment by performing actions and observing the results, which include the next state and the immediate reward [ 85 ]. AlphaZero, AlphaGo [ 113 ] are examples of the model-based approaches. On the other hand, a model-free approach does not use the distribution of the transition probability and the reward function associated with MDP. Q-learning, Deep Q Network, Monte Carlo Control, SARSA (State–Action–Reward–State–Action), etc. are some examples of model-free algorithms [ 52 ]. The policy network, which is required for model-based RL but not for model-free, is the key difference between model-free and model-based learning. In the following, we discuss the popular RL algorithms.

Monte Carlo methods: Monte Carlo techniques, or Monte Carlo experiments, are a wide category of computational algorithms that rely on repeated random sampling to obtain numerical results [ 52 ]. The underlying concept is to use randomness to solve problems that are deterministic in principle. Optimization, numerical integration, and making drawings from the probability distribution are the three problem classes where Monte Carlo techniques are most commonly used.

Q-learning: Q-learning is a model-free reinforcement learning algorithm for learning the quality of behaviors that tell an agent what action to take under what conditions [ 52 ]. It does not need a model of the environment (hence the term “model-free”), and it can deal with stochastic transitions and rewards without the need for adaptations. The ‘Q’ in Q-learning usually stands for quality, as the algorithm calculates the maximum expected rewards for a given behavior in a given state.

Deep Q-learning: The basic working step in Deep Q-Learning [ 52 ] is that the initial state is fed into the neural network, which returns the Q-value of all possible actions as an output. Still, when we have a reasonably simple setting to overcome, Q-learning works well. However, when the number of states and actions becomes more complicated, deep learning can be used as a function approximator.

Reinforcement learning, along with supervised and unsupervised learning, is one of the basic machine learning paradigms. RL can be used to solve numerous real-world problems in various fields, such as game theory, control theory, operations analysis, information theory, simulation-based optimization, manufacturing, supply chain logistics, multi-agent systems, swarm intelligence, aircraft control, robot motion control, and many more.

Artificial Neural Network and Deep Learning

Deep learning is part of a wider family of artificial neural networks (ANN)-based machine learning approaches with representation learning. Deep learning provides a computational architecture by combining several processing layers, such as input, hidden, and output layers, to learn from data [ 41 ]. The main advantage of deep learning over traditional machine learning methods is its better performance in several cases, particularly learning from large datasets [ 105 , 129 ]. Figure 9 shows a general performance of deep learning over machine learning considering the increasing amount of data. However, it may vary depending on the data characteristics and experimental set up.

Machine learning and deep learning performance in general with the amount of data

The most common deep learning algorithms are: Multi-layer Perceptron (MLP), Convolutional Neural Network (CNN, or ConvNet), Long Short-Term Memory Recurrent Neural Network (LSTM-RNN) [ 96 ]. In the following, we discuss various types of deep learning methods that can be used to build effective data-driven models for various purposes.

A structure of an artificial neural network modeling with multiple processing layers

MLP: The base architecture of deep learning, which is also known as the feed-forward artificial neural network, is called a multilayer perceptron (MLP) [ 82 ]. A typical MLP is a fully connected network consisting of an input layer, one or more hidden layers, and an output layer, as shown in Fig. 10 . Each node in one layer connects to each node in the following layer at a certain weight. MLP utilizes the “Backpropagation” technique [ 41 ], the most “fundamental building block” in a neural network, to adjust the weight values internally while building the model. MLP is sensitive to scaling features and allows a variety of hyperparameters to be tuned, such as the number of hidden layers, neurons, and iterations, which can result in a computationally costly model.

CNN or ConvNet: The convolution neural network (CNN) [ 65 ] enhances the design of the standard ANN, consisting of convolutional layers, pooling layers, as well as fully connected layers, as shown in Fig. 11 . As it takes the advantage of the two-dimensional (2D) structure of the input data, it is typically broadly used in several areas such as image and video recognition, image processing and classification, medical image analysis, natural language processing, etc. While CNN has a greater computational burden, without any manual intervention, it has the advantage of automatically detecting the important features, and hence CNN is considered to be more powerful than conventional ANN. A number of advanced deep learning models based on CNN can be used in the field, such as AlexNet [ 60 ], Xception [ 24 ], Inception [ 118 ], Visual Geometry Group (VGG) [ 44 ], ResNet [ 45 ], etc.

LSTM-RNN: Long short-term memory (LSTM) is an artificial recurrent neural network (RNN) architecture used in the area of deep learning [ 38 ]. LSTM has feedback links, unlike normal feed-forward neural networks. LSTM networks are well-suited for analyzing and learning sequential data, such as classifying, processing, and predicting data based on time series data, which differentiates it from other conventional networks. Thus, LSTM can be used when the data are in a sequential format, such as time, sentence, etc., and commonly applied in the area of time-series analysis, natural language processing, speech recognition, etc.

An example of a convolutional neural network (CNN or ConvNet) including multiple convolution and pooling layers

In addition to these most common deep learning methods discussed above, several other deep learning approaches [ 96 ] exist in the area for various purposes. For instance, the self-organizing map (SOM) [ 58 ] uses unsupervised learning to represent the high-dimensional data by a 2D grid map, thus achieving dimensionality reduction. The autoencoder (AE) [ 15 ] is another learning technique that is widely used for dimensionality reduction as well and feature extraction in unsupervised learning tasks. Restricted Boltzmann machines (RBM) [ 46 ] can be used for dimensionality reduction, classification, regression, collaborative filtering, feature learning, and topic modeling. A deep belief network (DBN) is typically composed of simple, unsupervised networks such as restricted Boltzmann machines (RBMs) or autoencoders, and a backpropagation neural network (BPNN) [ 123 ]. A generative adversarial network (GAN) [ 39 ] is a form of the network for deep learning that can generate data with characteristics close to the actual data input. Transfer learning is currently very common because it can train deep neural networks with comparatively low data, which is typically the re-use of a new problem with a pre-trained model [ 124 ]. A brief discussion of these artificial neural networks (ANN) and deep learning (DL) models are summarized in our earlier paper Sarker et al. [ 96 ].

Overall, based on the learning techniques discussed above, we can conclude that various types of machine learning techniques, such as classification analysis, regression, data clustering, feature selection and extraction, and dimensionality reduction, association rule learning, reinforcement learning, or deep learning techniques, can play a significant role for various purposes according to their capabilities. In the following section, we discuss several application areas based on machine learning algorithms.

Applications of Machine Learning

In the current age of the Fourth Industrial Revolution (4IR), machine learning becomes popular in various application areas, because of its learning capabilities from the past and making intelligent decisions. In the following, we summarize and discuss ten popular application areas of machine learning technology.

Predictive analytics and intelligent decision-making: A major application field of machine learning is intelligent decision-making by data-driven predictive analytics [ 21 , 70 ]. The basis of predictive analytics is capturing and exploiting relationships between explanatory variables and predicted variables from previous events to predict the unknown outcome [ 41 ]. For instance, identifying suspects or criminals after a crime has been committed, or detecting credit card fraud as it happens. Another application, where machine learning algorithms can assist retailers in better understanding consumer preferences and behavior, better manage inventory, avoiding out-of-stock situations, and optimizing logistics and warehousing in e-commerce. Various machine learning algorithms such as decision trees, support vector machines, artificial neural networks, etc. [ 106 , 125 ] are commonly used in the area. Since accurate predictions provide insight into the unknown, they can improve the decisions of industries, businesses, and almost any organization, including government agencies, e-commerce, telecommunications, banking and financial services, healthcare, sales and marketing, transportation, social networking, and many others.

Cybersecurity and threat intelligence: Cybersecurity is one of the most essential areas of Industry 4.0. [ 114 ], which is typically the practice of protecting networks, systems, hardware, and data from digital attacks [ 114 ]. Machine learning has become a crucial cybersecurity technology that constantly learns by analyzing data to identify patterns, better detect malware in encrypted traffic, find insider threats, predict where bad neighborhoods are online, keep people safe while browsing, or secure data in the cloud by uncovering suspicious activity. For instance, clustering techniques can be used to identify cyber-anomalies, policy violations, etc. To detect various types of cyber-attacks or intrusions machine learning classification models by taking into account the impact of security features are useful [ 97 ]. Various deep learning-based security models can also be used on the large scale of security datasets [ 96 , 129 ]. Moreover, security policy rules generated by association rule learning techniques can play a significant role to build a rule-based security system [ 105 ]. Thus, we can say that various learning techniques discussed in Sect. Machine Learning Tasks and Algorithms , can enable cybersecurity professionals to be more proactive inefficiently preventing threats and cyber-attacks.

Internet of things (IoT) and smart cities: Internet of Things (IoT) is another essential area of Industry 4.0. [ 114 ], which turns everyday objects into smart objects by allowing them to transmit data and automate tasks without the need for human interaction. IoT is, therefore, considered to be the big frontier that can enhance almost all activities in our lives, such as smart governance, smart home, education, communication, transportation, retail, agriculture, health care, business, and many more [ 70 ]. Smart city is one of IoT’s core fields of application, using technologies to enhance city services and residents’ living experiences [ 132 , 135 ]. As machine learning utilizes experience to recognize trends and create models that help predict future behavior and events, it has become a crucial technology for IoT applications [ 103 ]. For example, to predict traffic in smart cities, parking availability prediction, estimate the total usage of energy of the citizens for a particular period, make context-aware and timely decisions for the people, etc. are some tasks that can be solved using machine learning techniques according to the current needs of the people.

Traffic prediction and transportation: Transportation systems have become a crucial component of every country’s economic development. Nonetheless, several cities around the world are experiencing an excessive rise in traffic volume, resulting in serious issues such as delays, traffic congestion, higher fuel prices, increased CO \(_2\) pollution, accidents, emergencies, and a decline in modern society’s quality of life [ 40 ]. Thus, an intelligent transportation system through predicting future traffic is important, which is an indispensable part of a smart city. Accurate traffic prediction based on machine and deep learning modeling can help to minimize the issues [ 17 , 30 , 31 ]. For example, based on the travel history and trend of traveling through various routes, machine learning can assist transportation companies in predicting possible issues that may occur on specific routes and recommending their customers to take a different path. Ultimately, these learning-based data-driven models help improve traffic flow, increase the usage and efficiency of sustainable modes of transportation, and limit real-world disruption by modeling and visualizing future changes.

Healthcare and COVID-19 pandemic: Machine learning can help to solve diagnostic and prognostic problems in a variety of medical domains, such as disease prediction, medical knowledge extraction, detecting regularities in data, patient management, etc. [ 33 , 77 , 112 ]. Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus, according to the World Health Organization (WHO) [ 3 ]. Recently, the learning techniques have become popular in the battle against COVID-19 [ 61 , 63 ]. For the COVID-19 pandemic, the learning techniques are used to classify patients at high risk, their mortality rate, and other anomalies [ 61 ]. It can also be used to better understand the virus’s origin, COVID-19 outbreak prediction, as well as for disease diagnosis and treatment [ 14 , 50 ]. With the help of machine learning, researchers can forecast where and when, the COVID-19 is likely to spread, and notify those regions to match the required arrangements. Deep learning also provides exciting solutions to the problems of medical image processing and is seen as a crucial technique for potential applications, particularly for COVID-19 pandemic [ 10 , 78 , 111 ]. Overall, machine and deep learning techniques can help to fight the COVID-19 virus and the pandemic as well as intelligent clinical decisions making in the domain of healthcare.

E-commerce and product recommendations: Product recommendation is one of the most well known and widely used applications of machine learning, and it is one of the most prominent features of almost any e-commerce website today. Machine learning technology can assist businesses in analyzing their consumers’ purchasing histories and making customized product suggestions for their next purchase based on their behavior and preferences. E-commerce companies, for example, can easily position product suggestions and offers by analyzing browsing trends and click-through rates of specific items. Using predictive modeling based on machine learning techniques, many online retailers, such as Amazon [ 71 ], can better manage inventory, prevent out-of-stock situations, and optimize logistics and warehousing. The future of sales and marketing is the ability to capture, evaluate, and use consumer data to provide a customized shopping experience. Furthermore, machine learning techniques enable companies to create packages and content that are tailored to the needs of their customers, allowing them to maintain existing customers while attracting new ones.

NLP and sentiment analysis: Natural language processing (NLP) involves the reading and understanding of spoken or written language through the medium of a computer [ 79 , 103 ]. Thus, NLP helps computers, for instance, to read a text, hear speech, interpret it, analyze sentiment, and decide which aspects are significant, where machine learning techniques can be used. Virtual personal assistant, chatbot, speech recognition, document description, language or machine translation, etc. are some examples of NLP-related tasks. Sentiment Analysis [ 90 ] (also referred to as opinion mining or emotion AI) is an NLP sub-field that seeks to identify and extract public mood and views within a given text through blogs, reviews, social media, forums, news, etc. For instance, businesses and brands use sentiment analysis to understand the social sentiment of their brand, product, or service through social media platforms or the web as a whole. Overall, sentiment analysis is considered as a machine learning task that analyzes texts for polarity, such as “positive”, “negative”, or “neutral” along with more intense emotions like very happy, happy, sad, very sad, angry, have interest, or not interested etc.

Image, speech and pattern recognition: Image recognition [ 36 ] is a well-known and widespread example of machine learning in the real world, which can identify an object as a digital image. For instance, to label an x-ray as cancerous or not, character recognition, or face detection in an image, tagging suggestions on social media, e.g., Facebook, are common examples of image recognition. Speech recognition [ 23 ] is also very popular that typically uses sound and linguistic models, e.g., Google Assistant, Cortana, Siri, Alexa, etc. [ 67 ], where machine learning methods are used. Pattern recognition [ 13 ] is defined as the automated recognition of patterns and regularities in data, e.g., image analysis. Several machine learning techniques such as classification, feature selection, clustering, or sequence labeling methods are used in the area.

Sustainable agriculture: Agriculture is essential to the survival of all human activities [ 109 ]. Sustainable agriculture practices help to improve agricultural productivity while also reducing negative impacts on the environment [ 5 , 25 , 109 ]. The sustainable agriculture supply chains are knowledge-intensive and based on information, skills, technologies, etc., where knowledge transfer encourages farmers to enhance their decisions to adopt sustainable agriculture practices utilizing the increasing amount of data captured by emerging technologies, e.g., the Internet of Things (IoT), mobile technologies and devices, etc. [ 5 , 53 , 54 ]. Machine learning can be applied in various phases of sustainable agriculture, such as in the pre-production phase - for the prediction of crop yield, soil properties, irrigation requirements, etc.; in the production phase—for weather prediction, disease detection, weed detection, soil nutrient management, livestock management, etc.; in processing phase—for demand estimation, production planning, etc. and in the distribution phase - the inventory management, consumer analysis, etc.

User behavior analytics and context-aware smartphone applications: Context-awareness is a system’s ability to capture knowledge about its surroundings at any moment and modify behaviors accordingly [ 28 , 93 ]. Context-aware computing uses software and hardware to automatically collect and interpret data for direct responses. The mobile app development environment has been changed greatly with the power of AI, particularly, machine learning techniques through their learning capabilities from contextual data [ 103 , 136 ]. Thus, the developers of mobile apps can rely on machine learning to create smart apps that can understand human behavior, support, and entertain users [ 107 , 137 , 140 ]. To build various personalized data-driven context-aware systems, such as smart interruption management, smart mobile recommendation, context-aware smart searching, decision-making that intelligently assist end mobile phone users in a pervasive computing environment, machine learning techniques are applicable. For example, context-aware association rules can be used to build an intelligent phone call application [ 104 ]. Clustering approaches are useful in capturing users’ diverse behavioral activities by taking into account data in time series [ 102 ]. To predict the future events in various contexts, the classification methods can be used [ 106 , 139 ]. Thus, various learning techniques discussed in Sect. “ Machine Learning Tasks and Algorithms ” can help to build context-aware adaptive and smart applications according to the preferences of the mobile phone users.

In addition to these application areas, machine learning-based models can also apply to several other domains such as bioinformatics, cheminformatics, computer networks, DNA sequence classification, economics and banking, robotics, advanced engineering, and many more.

Challenges and Research Directions

Our study on machine learning algorithms for intelligent data analysis and applications opens several research issues in the area. Thus, in this section, we summarize and discuss the challenges faced and the potential research opportunities and future directions.

In general, the effectiveness and the efficiency of a machine learning-based solution depend on the nature and characteristics of the data, and the performance of the learning algorithms. To collect the data in the relevant domain, such as cybersecurity, IoT, healthcare and agriculture discussed in Sect. “ Applications of Machine Learning ” is not straightforward, although the current cyberspace enables the production of a huge amount of data with very high frequency. Thus, collecting useful data for the target machine learning-based applications, e.g., smart city applications, and their management is important to further analysis. Therefore, a more in-depth investigation of data collection methods is needed while working on the real-world data. Moreover, the historical data may contain many ambiguous values, missing values, outliers, and meaningless data. The machine learning algorithms, discussed in Sect “ Machine Learning Tasks and Algorithms ” highly impact on data quality, and availability for training, and consequently on the resultant model. Thus, to accurately clean and pre-process the diverse data collected from diverse sources is a challenging task. Therefore, effectively modifying or enhance existing pre-processing methods, or proposing new data preparation techniques are required to effectively use the learning algorithms in the associated application domain.

To analyze the data and extract insights, there exist many machine learning algorithms, summarized in Sect. “ Machine Learning Tasks and Algorithms ”. Thus, selecting a proper learning algorithm that is suitable for the target application is challenging. The reason is that the outcome of different learning algorithms may vary depending on the data characteristics [ 106 ]. Selecting a wrong learning algorithm would result in producing unexpected outcomes that may lead to loss of effort, as well as the model’s effectiveness and accuracy. In terms of model building, the techniques discussed in Sect. “ Machine Learning Tasks and Algorithms ” can directly be used to solve many real-world issues in diverse domains, such as cybersecurity, smart cities and healthcare summarized in Sect. “ Applications of Machine Learning ”. However, the hybrid learning model, e.g., the ensemble of methods, modifying or enhancement of the existing learning techniques, or designing new learning methods, could be a potential future work in the area.

Thus, the ultimate success of a machine learning-based solution and corresponding applications mainly depends on both the data and the learning algorithms. If the data are bad to learn, such as non-representative, poor-quality, irrelevant features, or insufficient quantity for training, then the machine learning models may become useless or will produce lower accuracy. Therefore, effectively processing the data and handling the diverse learning algorithms are important, for a machine learning-based solution and eventually building intelligent applications.

In this paper, we have conducted a comprehensive overview of machine learning algorithms for intelligent data analysis and applications. According to our goal, we have briefly discussed how various types of machine learning methods can be used for making solutions to various real-world issues. A successful machine learning model depends on both the data and the performance of the learning algorithms. The sophisticated learning algorithms then need to be trained through the collected real-world data and knowledge related to the target application before the system can assist with intelligent decision-making. We also discussed several popular application areas based on machine learning techniques to highlight their applicability in various real-world issues. Finally, we have summarized and discussed the challenges faced and the potential research opportunities and future directions in the area. Therefore, the challenges that are identified create promising research opportunities in the field which must be addressed with effective solutions in various application areas. Overall, we believe that our study on machine learning-based solutions opens up a promising direction and can be used as a reference guide for potential research and applications for both academia and industry professionals as well as for decision-makers, from a technical point of view.

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This article is part of the topical collection “Advances in Computational Approaches for Artificial Intelligence, Image Processing, IoT and Cloud Applications” guest edited by Bhanu Prakash K N and M. Shivakumar.

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Sarker, I.H. Machine Learning: Algorithms, Real-World Applications and Research Directions. SN COMPUT. SCI. 2 , 160 (2021). https://doi.org/10.1007/s42979-021-00592-x

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Received : 27 January 2021

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Published : 22 March 2021

DOI : https://doi.org/10.1007/s42979-021-00592-x

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Tight Convergence Rate Bounds for Optimization Under Power Law Spectral Conditions Maksim Velikanov, Dmitry Yarotsky , 2024. [ abs ][ pdf ][ bib ]

ptwt - The PyTorch Wavelet Toolbox Moritz Wolter, Felix Blanke, Jochen Garcke, Charles Tapley Hoyt , 2024. (Machine Learning Open Source Software Paper) [ abs ][ pdf ][ bib ]      [ code ]

Choosing the Number of Topics in LDA Models – A Monte Carlo Comparison of Selection Criteria Victor Bystrov, Viktoriia Naboka-Krell, Anna Staszewska-Bystrova, Peter Winker , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Functional Directed Acyclic Graphs Kuang-Yao Lee, Lexin Li, Bing Li , 2024. [ abs ][ pdf ][ bib ]

Unlabeled Principal Component Analysis and Matrix Completion Yunzhen Yao, Liangzu Peng, Manolis C. Tsakiris , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Distributed Estimation on Semi-Supervised Generalized Linear Model Jiyuan Tu, Weidong Liu, Xiaojun Mao , 2024. [ abs ][ pdf ][ bib ]

Towards Explainable Evaluation Metrics for Machine Translation Christoph Leiter, Piyawat Lertvittayakumjorn, Marina Fomicheva, Wei Zhao, Yang Gao, Steffen Eger , 2024. [ abs ][ pdf ][ bib ]

Differentially private methods for managing model uncertainty in linear regression Víctor Peña, Andrés F. Barrientos , 2024. [ abs ][ pdf ][ bib ]

Data Summarization via Bilevel Optimization Zalán Borsos, Mojmír Mutný, Marco Tagliasacchi, Andreas Krause , 2024. [ abs ][ pdf ][ bib ]

Pareto Smoothed Importance Sampling Aki Vehtari, Daniel Simpson, Andrew Gelman, Yuling Yao, Jonah Gabry , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Policy Gradient Methods in the Presence of Symmetries and State Abstractions Prakash Panangaden, Sahand Rezaei-Shoshtari, Rosie Zhao, David Meger, Doina Precup , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Scaling Instruction-Finetuned Language Models Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Yunxuan Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, Albert Webson, Shixiang Shane Gu, Zhuyun Dai, Mirac Suzgun, Xinyun Chen, Aakanksha Chowdhery, Alex Castro-Ros, Marie Pellat, Kevin Robinson, Dasha Valter, Sharan Narang, Gaurav Mishra, Adams Yu, Vincent Zhao, Yanping Huang, Andrew Dai, Hongkun Yu, Slav Petrov, Ed H. Chi, Jeff Dean, Jacob Devlin, Adam Roberts, Denny Zhou, Quoc V. Le, Jason Wei , 2024. [ abs ][ pdf ][ bib ]

Tangential Wasserstein Projections Florian Gunsilius, Meng Hsuan Hsieh, Myung Jin Lee , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Learnability of Linear Port-Hamiltonian Systems Juan-Pablo Ortega, Daiying Yin , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Off-Policy Action Anticipation in Multi-Agent Reinforcement Learning Ariyan Bighashdel, Daan de Geus, Pavol Jancura, Gijs Dubbelman , 2024. [ abs ][ pdf ][ bib ]      [ code ]

On Unbiased Estimation for Partially Observed Diffusions Jeremy Heng, Jeremie Houssineau, Ajay Jasra , 2024. (Machine Learning Open Source Software Paper) [ abs ][ pdf ][ bib ]      [ code ]

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions Stanislas Ducotterd, Alexis Goujon, Pakshal Bohra, Dimitris Perdios, Sebastian Neumayer, Michael Unser , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Mathematical Framework for Online Social Media Auditing Wasim Huleihel, Yehonathan Refael , 2024. [ abs ][ pdf ][ bib ]

An Embedding Framework for the Design and Analysis of Consistent Polyhedral Surrogates Jessie Finocchiaro, Rafael M. Frongillo, Bo Waggoner , 2024. [ abs ][ pdf ][ bib ]

Low-rank Variational Bayes correction to the Laplace method Janet van Niekerk, Haavard Rue , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Scaling the Convex Barrier with Sparse Dual Algorithms Alessandro De Palma, Harkirat Singh Behl, Rudy Bunel, Philip H.S. Torr, M. Pawan Kumar , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Causal-learn: Causal Discovery in Python Yujia Zheng, Biwei Huang, Wei Chen, Joseph Ramsey, Mingming Gong, Ruichu Cai, Shohei Shimizu, Peter Spirtes, Kun Zhang , 2024. (Machine Learning Open Source Software Paper) [ abs ][ pdf ][ bib ]      [ code ]

Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics Noga Mudrik, Yenho Chen, Eva Yezerets, Christopher J. Rozell, Adam S. Charles , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification Natalie S. Frank, Jonathan Niles-Weed , 2024. [ abs ][ pdf ][ bib ]

Data Thinning for Convolution-Closed Distributions Anna Neufeld, Ameer Dharamshi, Lucy L. Gao, Daniela Witten , 2024. [ abs ][ pdf ][ bib ]      [ code ]

A projected semismooth Newton method for a class of nonconvex composite programs with strong prox-regularity Jiang Hu, Kangkang Deng, Jiayuan Wu, Quanzheng Li , 2024. [ abs ][ pdf ][ bib ]

Revisiting RIP Guarantees for Sketching Operators on Mixture Models Ayoub Belhadji, Rémi Gribonval , 2024. [ abs ][ pdf ][ bib ]

Monotonic Risk Relationships under Distribution Shifts for Regularized Risk Minimization Daniel LeJeune, Jiayu Liu, Reinhard Heckel , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks Dong-Young Lim, Sotirios Sabanis , 2024. [ abs ][ pdf ][ bib ]

Axiomatic effect propagation in structural causal models Raghav Singal, George Michailidis , 2024. [ abs ][ pdf ][ bib ]

Optimal First-Order Algorithms as a Function of Inequalities Chanwoo Park, Ernest K. Ryu , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Resource-Efficient Neural Networks for Embedded Systems Wolfgang Roth, Günther Schindler, Bernhard Klein, Robert Peharz, Sebastian Tschiatschek, Holger Fröning, Franz Pernkopf, Zoubin Ghahramani , 2024. [ abs ][ pdf ][ bib ]

Trained Transformers Learn Linear Models In-Context Ruiqi Zhang, Spencer Frei, Peter L. Bartlett , 2024. [ abs ][ pdf ][ bib ]

Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees Nachuan Xiao, Xiaoyin Hu, Xin Liu, Kim-Chuan Toh , 2024. [ abs ][ pdf ][ bib ]

Efficient Modality Selection in Multimodal Learning Yifei He, Runxiang Cheng, Gargi Balasubramaniam, Yao-Hung Hubert Tsai, Han Zhao , 2024. [ abs ][ pdf ][ bib ]

A Multilabel Classification Framework for Approximate Nearest Neighbor Search Ville Hyvönen, Elias Jääsaari, Teemu Roos , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization Lorenzo Pacchiardi, Rilwan A. Adewoyin, Peter Dueben, Ritabrata Dutta , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Multiple Descent in the Multiple Random Feature Model Xuran Meng, Jianfeng Yao, Yuan Cao , 2024. [ abs ][ pdf ][ bib ]

Mean-Square Analysis of Discretized Itô Diffusions for Heavy-tailed Sampling Ye He, Tyler Farghly, Krishnakumar Balasubramanian, Murat A. Erdogdu , 2024. [ abs ][ pdf ][ bib ]

Invariant and Equivariant Reynolds Networks Akiyoshi Sannai, Makoto Kawano, Wataru Kumagai , 2024. (Machine Learning Open Source Software Paper) [ abs ][ pdf ][ bib ]      [ code ]

Personalized PCA: Decoupling Shared and Unique Features Naichen Shi, Raed Al Kontar , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee George H. Chen , 2024. [ abs ][ pdf ][ bib ]      [ code ]

On the Sample Complexity and Metastability of Heavy-tailed Policy Search in Continuous Control Amrit Singh Bedi, Anjaly Parayil, Junyu Zhang, Mengdi Wang, Alec Koppel , 2024. [ abs ][ pdf ][ bib ]

Convergence for nonconvex ADMM, with applications to CT imaging Rina Foygel Barber, Emil Y. Sidky , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms T. Tony Cai, Hongji Wei , 2024. [ abs ][ pdf ][ bib ]

Sparse NMF with Archetypal Regularization: Computational and Robustness Properties Kayhan Behdin, Rahul Mazumder , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Deep Network Approximation: Beyond ReLU to Diverse Activation Functions Shijun Zhang, Jianfeng Lu, Hongkai Zhao , 2024. [ abs ][ pdf ][ bib ]

Effect-Invariant Mechanisms for Policy Generalization Sorawit Saengkyongam, Niklas Pfister, Predrag Klasnja, Susan Murphy, Jonas Peters , 2024. [ abs ][ pdf ][ bib ]

Pygmtools: A Python Graph Matching Toolkit Runzhong Wang, Ziao Guo, Wenzheng Pan, Jiale Ma, Yikai Zhang, Nan Yang, Qi Liu, Longxuan Wei, Hanxue Zhang, Chang Liu, Zetian Jiang, Xiaokang Yang, Junchi Yan , 2024. (Machine Learning Open Source Software Paper) [ abs ][ pdf ][ bib ]      [ code ]

Heterogeneous-Agent Reinforcement Learning Yifan Zhong, Jakub Grudzien Kuba, Xidong Feng, Siyi Hu, Jiaming Ji, Yaodong Yang , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Sample-efficient Adversarial Imitation Learning Dahuin Jung, Hyungyu Lee, Sungroh Yoon , 2024. [ abs ][ pdf ][ bib ]

Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent Benjamin Gess, Sebastian Kassing, Vitalii Konarovskyi , 2024. [ abs ][ pdf ][ bib ]

Rates of convergence for density estimation with generative adversarial networks Nikita Puchkin, Sergey Samsonov, Denis Belomestny, Eric Moulines, Alexey Naumov , 2024. [ abs ][ pdf ][ bib ]

Additive smoothing error in backward variational inference for general state-space models Mathis Chagneux, Elisabeth Gassiat, Pierre Gloaguen, Sylvain Le Corff , 2024. [ abs ][ pdf ][ bib ]

Optimal Bump Functions for Shallow ReLU networks: Weight Decay, Depth Separation, Curse of Dimensionality Stephan Wojtowytsch , 2024. [ abs ][ pdf ][ bib ]

Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees Alexander Terenin, David R. Burt, Artem Artemev, Seth Flaxman, Mark van der Wilk, Carl Edward Rasmussen, Hong Ge , 2024. [ abs ][ pdf ][ bib ]      [ code ]

On Tail Decay Rate Estimation of Loss Function Distributions Etrit Haxholli, Marco Lorenzi , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu, Haizhao Yang, Minshuo Chen, Tuo Zhao, Wenjing Liao , 2024. [ abs ][ pdf ][ bib ]

Post-Regularization Confidence Bands for Ordinary Differential Equations Xiaowu Dai, Lexin Li , 2024. [ abs ][ pdf ][ bib ]

On the Generalization of Stochastic Gradient Descent with Momentum Ali Ramezani-Kebrya, Kimon Antonakopoulos, Volkan Cevher, Ashish Khisti, Ben Liang , 2024. [ abs ][ pdf ][ bib ]

Pursuit of the Cluster Structure of Network Lasso: Recovery Condition and Non-convex Extension Shotaro Yagishita, Jun-ya Gotoh , 2024. [ abs ][ pdf ][ bib ]

Iterate Averaging in the Quest for Best Test Error Diego Granziol, Nicholas P. Baskerville, Xingchen Wan, Samuel Albanie, Stephen Roberts , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Nonparametric Inference under B-bits Quantization Kexuan Li, Ruiqi Liu, Ganggang Xu, Zuofeng Shang , 2024. [ abs ][ pdf ][ bib ]

Black Box Variational Inference with a Deterministic Objective: Faster, More Accurate, and Even More Black Box Ryan Giordano, Martin Ingram, Tamara Broderick , 2024. [ abs ][ pdf ][ bib ]      [ code ]

On Sufficient Graphical Models Bing Li, Kyongwon Kim , 2024. [ abs ][ pdf ][ bib ]

Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond Nathan Kallus, Xiaojie Mao, Masatoshi Uehara , 2024. [ abs ][ pdf ][ bib ]      [ code ]

On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks Sebastian Neumayer, Lénaïc Chizat, Michael Unser , 2024. [ abs ][ pdf ][ bib ]

Improving physics-informed neural networks with meta-learned optimization Alex Bihlo , 2024. [ abs ][ pdf ][ bib ]

A Comparison of Continuous-Time Approximations to Stochastic Gradient Descent Stefan Ankirchner, Stefan Perko , 2024. [ abs ][ pdf ][ bib ]

Critically Assessing the State of the Art in Neural Network Verification Matthias König, Annelot W. Bosman, Holger H. Hoos, Jan N. van Rijn , 2024. [ abs ][ pdf ][ bib ]

Estimating the Minimizer and the Minimum Value of a Regression Function under Passive Design Arya Akhavan, Davit Gogolashvili, Alexandre B. Tsybakov , 2024. [ abs ][ pdf ][ bib ]

Modeling Random Networks with Heterogeneous Reciprocity Daniel Cirkovic, Tiandong Wang , 2024. [ abs ][ pdf ][ bib ]

Exploration, Exploitation, and Engagement in Multi-Armed Bandits with Abandonment Zixian Yang, Xin Liu, Lei Ying , 2024. [ abs ][ pdf ][ bib ]

On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture Models Yangjing Zhang, Ying Cui, Bodhisattva Sen, Kim-Chuan Toh , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Decorrelated Variable Importance Isabella Verdinelli, Larry Wasserman , 2024. [ abs ][ pdf ][ bib ]

Model-Free Representation Learning and Exploration in Low-Rank MDPs Aditya Modi, Jinglin Chen, Akshay Krishnamurthy, Nan Jiang, Alekh Agarwal , 2024. [ abs ][ pdf ][ bib ]

Seeded Graph Matching for the Correlated Gaussian Wigner Model via the Projected Power Method Ernesto Araya, Guillaume Braun, Hemant Tyagi , 2024. [ abs ][ pdf ][ bib ]      [ code ]

Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization Shicong Cen, Yuting Wei, Yuejie Chi , 2024. [ abs ][ pdf ][ bib ]

Power of knockoff: The impact of ranking algorithm, augmented design, and symmetric statistic Zheng Tracy Ke, Jun S. Liu, Yucong Ma , 2024. [ abs ][ pdf ][ bib ]

Lower Complexity Bounds of Finite-Sum Optimization Problems: The Results and Construction Yuze Han, Guangzeng Xie, Zhihua Zhang , 2024. [ abs ][ pdf ][ bib ]

On Truthing Issues in Supervised Classification Jonathan K. Su , 2024. [ abs ][ pdf ][ bib ]

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10 Must Read Machine Learning Research Papers

Machine learning is a rapidly evolving field with research papers often serving as the foundation for discoveries and advancements. For anyone keen to delve into the theoretical and practical aspects of machine learning, the following ten research papers are essential reads. They cover foundational concepts, groundbreaking techniques, and key advancements in the field.

This article highlights 10 must-read machine learning research papers that have significantly contributed to the development and understanding of machine learning. Whether you’re a beginner or an experienced practitioner, these papers provide invaluable insights that will help you grasp the complexities of machine learning and its potential to transform industries.

Table of Content

1. “A Few Useful Things to Know About Machine Learning” by Pedro Domingos

2. “imagenet classification with deep convolutional neural networks” by alex krizhevsky, ilya sutskever, and geoffrey e. hinton, 3. “playing atari with deep reinforcement learning” by volodymyr mnih et al., 4. “sequence to sequence learning with neural networks” by ilya sutskever, oriol vinyals, and quoc v. le, 5. “attention is all you need” by ashish vaswani et al., 6. “generative adversarial nets” by ian goodfellow et al., 7. “bert: pre-training of deep bidirectional transformers for language understanding” by jacob devlin et al., 8. “deep residual learning for image recognition” by kaiming he et al., 9. “a survey on deep learning in medical image analysis” by geert litjens et al., 10. “alphago: mastering the game of go with deep neural networks and tree search” by silver et al..

Summary : Pedro Domingos provides a comprehensive overview of essential machine learning concepts and common pitfalls. This paper is a great starting point for understanding the broader landscape of machine learning.

Key Contributions:

• Distills core principles and practical advice.
• Discusses overfitting, feature engineering, and model selection.
• Offers insights into the trade-offs between different machine learning algorithms.

Access: Read the Paper

Summary : Often referred to as the “AlexNet” paper, this work introduced a deep convolutional neural network that significantly improved image classification benchmarks, marking a turning point in computer vision.

• Demonstrated the power of deep learning for image classification.
• Introduced techniques like dropout and ReLU activations.
• Showed the importance of large-scale datasets and GPU acceleration.

Summary : This paper from DeepMind presents the use of deep Q-networks (DQN) to play Atari games . It was a seminal work in applying deep learning to reinforcement learning.

• Introduced the concept of using deep learning for Q-learning.
• Showcased the ability of DQNs to learn complex behaviors from raw pixel data.
• Paved the way for further research in reinforcement learning.

Summary : This paper introduced the sequence-to-sequence (seq2seq) learning framework , which has become fundamental for tasks such as machine translation and text summarization.

• Proposed an encoder-decoder architecture for sequence tasks.
• Demonstrated effective training of neural networks for sequence modeling.
• Laid the groundwork for subsequent advancements in natural language processing.

Summary : This paper introduces the Transformer model, which relies solely on attention mechanisms, discarding recurrent layers used in previous models. It has become the backbone of many modern NLP systems.

• Proposed the Transformer architecture, which uses self-attention to capture dependencies.
• Demonstrated improvements in training efficiency and performance over RNN-based models.
• Led to the development of models like BERT, GPT, and others.

Summary : Ian Goodfellow and his colleagues introduced Generative Adversarial Networks (GANs) , a revolutionary framework for generating realistic data through adversarial training.

• Proposed a novel approach where two neural networks compete against each other.
• Enabled the generation of high-quality images, text, and other data types.
• Spurred a plethora of research on GAN variations and applications.

Summary : BERT (Bidirectional Encoder Representations from Transformers) introduced a new way of pre-training language models, significantly improving performance on various NLP benchmarks.

• Proposed bidirectional training of transformers to capture context from both directions.
• Achieved state-of-the-art results on several NLP tasks.
• Set the stage for subsequent models like RoBERTa, ALBERT, and DistilBERT.

Summary : This paper introduces Residual Networks (ResNets), which utilize residual learning to train very deep neural networks effectively.

• Addressed the issue of vanishing gradients in very deep networks.
• Demonstrated that extremely deep networks can be trained successfully.
• Improved performance on image classification tasks and influenced subsequent network architectures.

Summary : This survey provides a comprehensive review of deep learning techniques applied to medical image analysis, summarizing the state of the art in this specialized field.

• Reviewed various deep learning methods used in medical imaging.
• Discussed challenges and future directions in the field.
• Provided insights into applications such as disease detection and image segmentation.

Summary : This paper describes AlphaGo, the first AI to defeat a world champion in the game of Go, using a combination of deep neural networks and Monte Carlo tree search.

• Demonstrated the effectiveness of combining deep learning with traditional search techniques.
• Achieved a major milestone in AI by mastering a complex game.
• Influenced research in AI and its application to other complex decision-making problems.

These ten research papers cover a broad spectrum of machine learning advancements, from foundational concepts to cutting-edge techniques. They provide valuable insights into the development and application of machine learning technologies, making them essential reads for anyone looking to deepen their understanding of the field. By exploring these papers, you can gain a comprehensive view of how machine learning has evolved and where it might be heading in the future.

10 Must Read Machine Learning Research Papers – FAQ’s

What are large language models (llms) and why are they important.

Large Language Models (LLMs) are advanced AI systems designed to understand and generate human language. They are built using deep learning techniques, particularly transformer architectures. LLMs are important because they enable applications such as text generation, translation, and sentiment analysis, significantly advancing the field of natural language processing (NLP).

Why should I read “A Few Useful Things to Know About Machine Learning” by Pedro Domingos?

Pedro Domingos’ paper provides a broad overview of key machine learning concepts, common challenges, and practical advice. It’s an excellent resource for both beginners and experienced practitioners to understand the underlying principles of machine learning and avoid common pitfalls.

What impact did “ImageNet Classification with Deep Convolutional Neural Networks” have on the field?

The “AlexNet” paper revolutionized image classification by demonstrating the effectiveness of deep convolutional neural networks. It significantly improved benchmark results on ImageNet and introduced techniques like dropout and ReLU activations, which are now standard in deep learning.

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Popular Machine Learning papers on Papers with Code

Here is the list of the popular machine learning papers on Papers with Code with some remarkable methods and modules in machine learning.

The world now realizes the value of machine learning algorithms in computing and forecasting, which has fueled a boom in machine learning research. According to the data mining blog , roughly 100 machine learning papers are published in a day on Arxiv, a well-known public repository of research papers. There are more open repositories, including Paper with Code, Crossminds, Connected Papers, and others. 

Papers with Code is a website organizing free access to technical published papers and providing the software used in the papers. The objective of the website is to create a free and open resource for machine learning and computer vision researchers, including machine learning papers, code, datasets, methods, and evaluation tables. These resources are provided with the support of the natural language processing and machine learning community. Papers with Code has 79,817 papers, 9,327 benchmarks, and 3,681 tasks till now, and we expect to see more state-of-art papers in the future. Some significant methods and modules are popular for research and study in these papers. Here is the list of the popular machine learning papers on Papers with Code.

List of top machine learning papers on Papers with Code

This list contains the top 10 machine learning papers available on Papers with Code. 

1. TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning

“TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning” paper introduces TensorFlow Eager, a multi-stage Python-embedded domain-specific language for hardware accelerated machine learning suitable for both interactive research and production. TensorFlow has shown remarkable performance but requires users to represent competitions as dataflow graphs, hindering rapid prototyping and run-time dynamism. On the contrary, TensorFlow Eager excels TensorFlow and eliminates the usability cost without sacrificing the benefits of graphs. TensorFlow Eager provides a crucial front-end to TensorFlow used to execute operations immediately and a JIT tracker translating Python functions composed of TensorFlow operations. The paper concludes by providing TensorFlow Eager that is easier to interpolate between imperative and staged execution in a single package.

Link to the paper: TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning 

Code: GitHub

2. A Simple Single-Scale Vision Transformer for Object Localization and Instance Segmentation 

The “A Simple Single-Scale Vision Transformer for Object Localization and Instance Segmentation” paper put forth a simple vision transformer design to use object localization and instance segmentation tasks. With the adaptation of vision transformer (ViT) for object detection and dense prediction tasks, many models inherited multistage designs. The multi-stage design provides a better trade-off among computational costs and effective aggregation of multiscale global contexts. This paper comprises three architectural options in ViT: spatial reduction, doubled channels, and multiscale features, demonstrating that a vanilla ViT architecture can provide a better trade-off without multiscale features. Additionally, the paper proposes a simple and compact ViT architecture called Universal Vision Transformer (UViT) to achieve high performance on common objects in context (COCO) object detection and instance segmentation tasks.

Link to the paper: A Simple Single-Scale Vision Transformer for Object Localization and Instance Segmentation

3. Visual Attention Network 

“Visual Attention Network” paper proposes a novel linear attention named large kernel attention (LKA). LKA enables the self-adaptive and long-range correlations in self-attention while avoiding the three shortcomings: training images as 1D sequences neglecting their 2D structures, quadratic complexity is too expensive, and capturing only spatial adaptability but ignores channel adaptability. This research paper is authored by Meng-Hao Guo, Cheng-Ze Lu, Zheng-Ning Liu, Ming-Ming Cheng, and Shi-Min Hu. The research is an attention VAN based on LKA, which is similar to ViTs and convolutional neural networks (CNNs). This paper shows that VANs outperform ViTs and CNNs in extensive experiments for tasks like image classification, semantic segmentation, pose estimation, and more. 

Link to the paper: Visual Attention Network

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4. A ConvNet for the 2020s

The “A ConvNet for the 2020s” paper revolves around visual recognition tasks and introduces vision transformers or ViTs. The ViTs were found to overthrow ConNets or CNNs, the state-of-the-art image classification models in the 20s. Although ViTs showed great performance and gained popularity, ViTs got issues when applied to general computer vision tasks like objection detection and semantic segmentation. This paper contains the diligence of Zhuang Liu, Hanzi Mao, Chao-yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie to reexamine design spaces and test a pure ConvNet. The paper shows a gradual modernization of a standard residual network (ResNet), directing it to the design of a vision transformer. The conclusion of the paper brings out a family of pure ConvNet models called ConvNeXt. ConvNeXt models are entirely constructed in ConvNet and use depthwise convolution, which can achieve accuracy and scalability similar to transformers or even outperforms the vision transformers.

Link to the paper: A ConvNet for the 2020s

5. Scikit-learn: Machine Learning in Python 

“Scikit-learn: Machine Learning in Python” is an old research paper released in 2012 that proposes the famous Python module Scikit-learn or Sklearn. The module integrates a wide range of state-of-the-art machine learning algorithms for medium-scaled supervised and unsupervised learning tasks. The creation of Sklearn was done by David Cournapeau, who is a co-author of this paper, and a group of researchers known as the Scikit-learn community. Also, the Scikit-learn website provides source code, binaries, and documentation. The package aims to help non-specialists implement machine learning using a high-level language. The focus of the paper remains on the package being user-friendly, great performance, documentation, and API consistency. The outcome of the paper is the popular Scikit-learn module which makes an essential Python library for building machine learning models today. 

Link to the paper: Scikit-learn: Machine Learning in Python

6. Adapting the Tesseract Open Source OCR Engine for Multilingual OCR

“Adapting the Tesseract Open Source OCR Engine for Multilingual OCR” is the machine learning paper where the authors Ray Smith, Daria Antonova, and Dar-Shyang Lee describe efforts to adapt the Tesseract open source optical character recognition (OCR) engine for multiple scripts and languages. The focus was centered on enabling generic multi-lingual operation, so there is negligible customization for new language beyond providing a corpus of text. The paper concluded to find that the Tesseract classifier easily adapts to simplified Chinese, and tests on English, European, and Russian languages were run and calculated a consistent word error rate between 3.72% to 5.78%.

Link to the paper: Adapting the Tesseract Open Source OCR Engine for Multilingual OCR

Code: GitHub  

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7. COLD: A Benchmark for Chinese Offensive Language Detection

To maintain a healthy and safe social platform, offensive language detection and prevention models are important. Although much research is conducted on offensive language detection and prevention, most studies only focus on English. In the paper “COLD: A Benchmark for Chinese Offensive Language Detection,” Jiawen Deng, Jingyan Zhou, Hao Sun, Fei Mi, and Minlie Huang facilitate to create and evaluate a Chinese offensive language detection model. Here, the COLDataset is used, which is a Chinese offensive language dataset consisting of 37k annotated sentences, and to detect offensive language, a baseline classifier called COLDetector is used, having 81% accuracy. The paper concludes with two main findings around the popular Chinese language models, CPM and CDialGPT. The findings are that the CPM tends to give more offensive output in comparison to CDialGPT, and certain prompts such as anti-bias sentences, trigger the offensive outputs. 

Link to the paper: COLD: A Benchmark for Chinese Offensive Language Detection

8. Gender Classification and Bias Mitigation in Facial Images 

Gender classification algorithms are useful in domains like demographic research, law enforcement, and human-computer interaction. Recent research showed two issues in gender classification, biased benchmark datasets result in algorithmic bias, and the emergence of gender minorities like LGBTQ and non-binary has been left out in gender classification. The paper “Gender Classification and Bias Mitigation in Facial Images” sheds light on the two issues mentioned above. Through surveys conducted under this paper, it was discovered that the current benchmark datasets lack representation of gender minority subgroups, so bias occurs. Here, two new facial image databases were created, a radically balanced inclusive database with the addition of LGBTQ subset and an inclusive gender database collectively with non-binary people. In the paper, an ensemble model was created and evaluated, producing an accuracy of 90.39%.

Link to the paper: Gender Classification and Bias Mitigation in Facial Images

9. DeepFaceLab: Integrated, flexible and extensible face-swapping framework

Deepfake defense requires research of detection and the efforts of generation methods, and the current Deepfake methods have obscure workflow and poor performance. The “DeepFaceLab: Integrated, flexible and extensible face-swapping framework” paper introduces DeepFaceLab as a solution to Deepfake defense issues. DeepFaceLab is the current dominant deepfake framework with the necessary tools to conduct high-quality face-swapping. Here, the focus is on the implementation of DeepFaceLab with detailed principles and introduces the whole control over pipeline from where one can modify to have customized pipelines. The performance of DeepFaceLab is excellent, and it can achieve cinema-quality results with high fidelity. 

Link to the paper: DeepFaceLab: Integrated, flexible and extensible face-swapping framework

10. Generalized End-to-End Loss for Speaker Verification

“Generalized End-to-End Loss for Speaker Verification” paper proposes a new loss function called the generalized end-to-end (GE2E) loss. This paper found that the GE2E loss function is more efficient than previous tuple-based end-to-end (TE2E) loss functions in the training of speaker verification models. GE2E loss function updates the network focusing on examples that are difficult to verify at each step of training and so do not require the initial stage of example selection. With the GE2E loss function, the model decreases speaker verification EER by more than 10% and simultaneously reduces the training time by 60%. Also, the paper introduces the MultiReader technique allowing domain adaptation, in which a model can be trained more accurately with the support of multiple keywords and multiple dialects. 

Link to the paper: Generalized End-to-End Loss for Speaker Verification

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• DOI: 10.2196/59587
• Corpus ID: 269185679

Data Preprocessing Techniques for Artificial Learning (AI)/Machine Learning (ML)-Readiness: Systematic Review of Wearable Sensor Data in Cancer Care.

• Bengie L. Ortiz , Vibhuti Gupta , +6 authors Muneesh Tewari
• Published in JMIR mHealth and uHealth 16 April 2024
• Medicine, Computer Science

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Large language models for wearable sensor-based human activity recognition, health monitoring, and behavioral modeling: a survey of early trends, datasets, and challenges, 89 references, dyadic and individual variation in 24-hour heart rates of cancer patients and their caregivers, an innovative non-invasive approach to personalized nutrition and metabolism monitoring using wearable sensors, evaluating the potential of machine learning and wearable devices in end-of-life care in predicting 7-day death events among patients with terminal cancer: cohort study, physical fitness assessment for cancer patients using multi-model decision fusion based on multi-source data, updating the definition of cancer, daily physical activity monitoring in older adults with metastatic prostate cancer on active treatment: feasibility and associations with toxicity., assessing upper limb function in breast cancer survivors using wearable sensors and machine learning in a free-living environment, wearable based monitoring and self-supervised contrastive learning detect clinical complications during treatment of hematologic malignancies, machine learning for postoperative continuous recovery scores of oncology patients in perioperative care with data from wearables, persistent homology-based machine learning method for filtering and classifying mammographic microcalcification images in early cancer detection, related papers.

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Title: machine learning for predicting control landscape maps of quantum molecular dynamics: laser-induced three-dimensional alignment of asymmetric top molecules.

Abstract: Machine learning for predicting control landscape maps of full quantum molecular dynamics is examined through a case study of the laser-induced three-dimensional (3D) alignment of asymmetric top molecules, an essential technique for observing and/or manipulating molecular dynamics in a molecule-fixed frame. We consider the "prolate-type" asymmetryic top molecules with the asymmetry parameters $-1 < \kappa < 0$ and the C2v symmetry in the low-temperature limiting case, which are aligned by using mutually orthogonal linearly polarized double laser pulses. The landscape map for each molecule consists of 6000 pixels, each pixel of which represents the maximum degree of alignment achieved by each set of control parameters. After examining ways to deal with the markedly different molecular parameters in a unified manner for suitably training a convolutional neural network (CNN) model, we train the CNN model by using 55 training sample molecules to predict the control landscape maps of 35 test sample molecules with reasonably high accuracy. As the predicted landscape maps provide a big picture of the alignment control, we show, for example, that the double pulse control scheme is especially effective for a molecule having a polarizability component that is much larger in value than the other two components.

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• Published: 22 July 2024

Neural general circulation models for weather and climate

• Dmitrii Kochkov   ORCID: orcid.org/0000-0003-3846-4911 1   na1 ,
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• Atmospheric dynamics
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General circulation models (GCMs) are the foundation of weather and climate prediction 1 , 2 . GCMs are physics-based simulators that combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine-learning models trained on reanalysis data have achieved comparable or better skill than GCMs for deterministic weather forecasting 3 , 4 . However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present a GCM that combines a differentiable solver for atmospheric dynamics with machine-learning components and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best machine-learning and physics-based methods. NeuralGCM is competitive with machine-learning models for one- to ten-day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for one- to fifteen-day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics for multiple decades, and climate forecasts with 140-kilometre resolution show emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs, although our model does not extrapolate to substantially different future climates. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

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Solving the equations for Earth’s atmosphere with general circulation models (GCMs) is the basis of weather and climate prediction 1 , 2 . Over the past 70 years, GCMs have been steadily improved with better numerical methods and more detailed physical models, while exploiting faster computers to run at higher resolution. Inside GCMs, the unresolved physical processes such as clouds, radiation and precipitation are represented by semi-empirical parameterizations. Tuning GCMs to match historical data remains a manual process 5 , and GCMs retain many persistent errors and biases 6 , 7 , 8 . The difficulty of reducing uncertainty in long-term climate projections 9 and estimating distributions of extreme weather events 10 presents major challenges for climate mitigation and adaptation 11 .

Recent advances in machine learning have presented an alternative for weather forecasting 3 , 4 , 12 , 13 . These models rely solely on machine-learning techniques, using roughly 40 years of historical data from the European Center for Medium-Range Weather Forecasts (ECMWF) reanalysis v5 (ERA5) 14 for model training and forecast initialization. Machine-learning methods have been remarkably successful, demonstrating state-of-the-art deterministic forecasts for 1- to 10-day weather prediction at a fraction of the computational cost of traditional models 3 , 4 . Machine-learning atmospheric models also require considerably less code, for example GraphCast 3 has 5,417 lines versus 376,578 lines for the National Oceanic and Atmospheric Administration’s FV3 atmospheric model 15 (see Supplementary Information section  A for details).

Nevertheless, machine-learning approaches have noteworthy limitations compared with GCMs. Existing machine-learning models have focused on deterministic prediction, and surpass deterministic numerical weather prediction in terms of the aggregate metrics for which they are trained 3 , 4 . However, they do not produce calibrated uncertainty estimates 4 , which is essential for useful weather forecasts 1 . Deterministic machine-learning models using a mean-squared-error loss are rewarded for averaging over uncertainty, producing unrealistically blurry predictions when optimized for multi-day forecasts 3 , 13 . Unlike physical models, machine-learning models misrepresent derived (diagnostic) variables such as geostrophic wind 16 . Furthermore, although there has been some success in using machine-learning approaches on longer timescales 17 , 18 , these models have not demonstrated the ability to outperform existing GCMs.

Hybrid models that combine GCMs with machine learning are appealing because they build on the interpretability, extensibility and successful track record of traditional atmospheric models 19 , 20 . In the hybrid model approach, a machine-learning component replaces or corrects the traditional physical parameterizations of a GCM. Until now, the machine-learning component in such models has been trained ‘offline’, by learning parameterizations independently of their interaction with dynamics. These components are then inserted into an existing GCM. The lack of coupling between machine-learning components and the governing equations during training potentially causes serious problems, such as instability and climate drift 21 . So far, hybrid models have mostly been limited to idealized scenarios such as aquaplanets 22 , 23 . Under realistic conditions, machine-learning corrections have reduced some biases of very coarse GCMs 24 , 25 , 26 , but performance remains considerably worse than state-of-the-art models.

Here we present NeuralGCM, a fully differentiable hybrid GCM of Earth’s atmosphere. NeuralGCM is trained on forecasting up to 5-day weather trajectories sampled from ERA5. Differentiability enables end-to-end ‘online training’ 27 , with machine-learning components optimized in the context of interactions with the governing equations for large-scale dynamics, which we find enables accurate and stable forecasts. NeuralGCM produces physically consistent forecasts with accuracy comparable to best-in-class models across a range of timescales, from 1- to 15-day weather to decadal climate prediction.

Neural GCMs

A schematic of NeuralGCM is shown in Fig. 1 . The two key components of NeuralGCM are a differentiable dynamical core for solving the discretized governing dynamical equations and a learned physics module that parameterizes physical processes with a neural network, described in full detail in Methods , Supplementary Information sections  B and C , and Supplementary Table 1 . The dynamical core simulates large-scale fluid motion and thermodynamics under the influence of gravity and the Coriolis force. The learned physics module (Supplementary Fig. 1 ) predicts the effect of unresolved processes, such as cloud formation, radiative transport, precipitation and subgrid-scale dynamics, on the simulated fields using a neural network.

a , Overall model structure, showing how forcings F t , noise z t (for stochastic models) and inputs y t are encoded into the model state x t . The model state is fed into the dynamical core, and alongside forcings and noise into the learned physics module. This produces tendencies (rates of change) used by an implicit–explicit ordinary differential equation (ODE) solver to advance the state in time. The new model state x t +1 can then be fed back into another time step, or decoded into model predictions. b , The learned physics module, which feeds data for individual columns of the atmosphere into a neural network used to produce physics tendencies in that vertical column.

The differentiable dynamical core in NeuralGCM allows an end-to-end training approach, whereby we advance the model multiple time steps before employing stochastic gradient descent to minimize discrepancies between model predictions and reanalysis (Supplementary Information section  G.2 ). We gradually increase the rollout length from 6 hours to 5 days (Supplementary Information section  G and Supplementary Table 5 ), which we found to be critical because our models are not accurate for multi-day prediction or stable for long rollouts early in training (Supplementary Information section  H.6.2 and Supplementary Fig. 23 ). The extended back-propagation through hundreds of simulation steps enables our neural networks to take into account interactions between the learned physics and the dynamical core. We train deterministic and stochastic NeuralGCM models, each of which uses a distinct training protocol, described in full detail in Methods and Supplementary Table 4 .

We train a range of NeuralGCM models at horizontal resolutions with grid spacing of 2.8°, 1.4° and 0.7° (Supplementary Fig. 7 ). We evaluate the performance of NeuralGCM at a range of timescales appropriate for weather forecasting and climate simulation. For weather, we compare against the best-in-class conventional physics-based weather models, ECMWF’s high-resolution model (ECMWF-HRES) and ensemble prediction system (ECMWF-ENS), and two of the recent machine-learning-based approaches, GraphCast 3 and Pangu 4 . For climate, we compare against a global cloud-resolving model and Atmospheric Model Intercomparison Project (AMIP) runs.

Medium-range weather forecasting

Our evaluation set-up focuses on quantifying accuracy and physical consistency, following WeatherBench2 12 . We regrid all forecasts to a 1.5° grid using conservative regridding, and average over all 732 forecasts made at noon and midnight UTC in the year 2020, which was held-out from training data for all machine-learning models. NeuralGCM, GraphCast and Pangu compare with ERA5 as the ground truth, whereas ECMWF-ENS and ECMWF-HRES compare with the ECMWF operational analysis (that is, HRES at 0-hour lead time), to avoid penalizing the operational forecasts for different biases than ERA5.

Model accuracy

We use ECMWF’s ensemble (ENS) model as a reference baseline as it achieves the best performance across the majority of lead times 12 . We assess accuracy using (1) root-mean-squared error (RMSE), (2) root-mean-squared bias (RMSB), (3) continuous ranked probability score (CRPS) and (4) spread-skill ratio, with the results shown in Fig. 2 . We provide more in-depth evaluations including scorecards, metrics for additional variables and levels and maps in Extended Data Figs. 1 and 2 , Supplementary Information section  H and Supplementary Figs. 9 – 22 .

a , c , RMSE ( a ) and RMSB ( c ) for ECMWF-ENS, ECMWF-HRES, NeuralGCM-0.7°, NeuralGCM-ENS, GraphCast 3 and Pangu 4 on headline WeatherBench2 variables, as a percentage of the error of ECMWF-ENS. Deterministic and stochastic models are shown in solid and dashed lines respectively. e , g , CRPS relative to ECMWF-ENS ( e ) and spread-skill ratio for the ENS and NeuralGCM-ENS models ( g ). b , d , f , h , Spatial distributions of RMSE ( b ), bias ( d ), CRPS ( f ) and spread-skill ratio ( h ) for NeuralGCM-ENS and ECMWF-ENS models for 10-day forecasts of specific humidity at 700 hPa. Spatial plots of RMSE and CRPS show skill relative to a probabilistic climatology 12 with an ensemble member for each of the years 1990–2019. The grey areas indicate regions where climatological surface pressure on average is below 700 hPa.

Deterministic models that produce a single weather forecast for given initial conditions can be compared effectively using RMSE skill at short lead times. For the first 1–3 days, depending on the atmospheric variable, RMSE is minimized by forecasts that accurately track the evolution of weather patterns. At this timescale we find that NeuralGCM-0.7° and GraphCast achieve best results, with slight variations across different variables (Fig. 2a ). At longer lead times, RMSE rapidly increases owing to chaotic divergence of nearby weather trajectories, making RMSE less informative for deterministic models. RMSB calculates persistent errors over time, which provides an indication of how models would perform at much longer lead times. Here NeuralGCM models also compare favourably against previous approaches (Fig. 2c ), with notably much less bias for specific humidity in the tropics (Fig. 2d ).

Ensembles are essential for capturing intrinsic uncertainty of weather forecasts, especially at longer lead times. Beyond about 7 days, the ensemble means of ECMWF-ENS and NeuralGCM-ENS forecasts have considerably lower RMSE than the deterministic models, indicating that these models better capture the average of possible weather. A better metric for ensemble models is CRPS, which is a proper scoring rule that is sensitive to full marginal probability distributions 28 . Our stochastic model (NeuralGCM-ENS) running at 1.4° resolution has lower error compared with ECMWF-ENS across almost all variables, lead times and vertical levels for ensemble-mean RMSE, RSMB and CRPS (Fig. 2a,c,e and Supplementary Information section  H ), with similar spatial patterns of skill (Fig. 2b,f ). Like ECMWF-ENS, NeuralGCM-ENS has a spread-skill ratio of approximately one (Fig. 2d ), which is a necessary condition for calibrated forecasts 29 .

An important characteristic of forecasts is their resemblance to realistic weather patterns. Figure 3 shows a case study that illustrates the performance of NeuralGCM on three types of important weather phenomenon: tropical cyclones, atmospheric rivers and the Intertropical Convergence Zone. Figure 3a shows that all the machine-learning models make significantly blurrier forecasts than the source data ERA5 and physics-based ECMWF-HRES forecast, but NeuralCGM-0.7° outperforms the pure machine-learning models, despite its coarser resolution (0.7° versus 0.25° for GraphCast and Pangu). Blurry forecasts correspond to physically inconsistent atmospheric conditions and misrepresent extreme weather. Similar trends hold for other derived variables of meteorological interest (Supplementary Information section  H.2 ). Ensemble-mean predictions, from both NeuralGCM and ECMWF, are closer to ERA5 in an average sense, and thus are inherently smooth at long lead times. In contrast, as shown in Fig. 3 and in Supplementary Information section  H.3 , individual realizations from the ECMWF and NeuralGCM ensembles remain sharp, even at long lead times. Like ECMWF-ENS, NeuralGCM-ENS produces a statistically representative range of future weather scenarios for each weather phenomenon, despite its eight-times-coarser resolution.

All forecasts are initialized at 2020-08-22T12z, chosen to highlight Hurricane Laura, the most damaging Atlantic hurricane of 2020. a , Specific humidity at 700 hPa for 1-day, 5-day and 10-day forecasts over North America and the Northeast Pacific Ocean from ERA5 14 , ECMWF-HRES, NeuralGCM-0.7°, ECMWF-ENS (mean), NeuralGCM-ENS (mean), GraphCast 3 and Pangu 4 . b , Forecasts from individual ensemble members from ECMWF-ENS and NeuralGCM-ENS over regions of interest, including predicted tracks of Hurricane Laura from each of the 50 ensemble members (Supplementary Information section  I.2 ). The track from ERA5 is plotted in black.

We can quantify the blurriness of different forecast models via their power spectra. Supplementary Figs. 17 and 18 show that the power spectra of NeuralCGM-0.7° is consistently closer to ERA5 than the other machine-learning forecast methods, but is still blurrier than ECMWF’s physical forecasts. The spectra of NeuralGCM forecasts is also roughly constant over the forecast period, in stark contrast to GraphCast, which worsens with lead time. The spectrum of NeuralGCM becomes more accurate with increased resolution (Supplementary Fig. 22 ), which suggests the potential for further improvements of NeuralGCM models trained at higher resolutions.

Water budget

In NeuralGCM, advection is handled by the dynamical core, while the machine-learning parameterization models local processes within vertical columns of the atmosphere. Thus, unlike pure machine-learning methods, local sources and sinks can be isolated from tendencies owing to horizontal transport and other resolved dynamics (Supplementary Fig. 3 ). This makes our results more interpretable and facilitates the diagnosis of the water budget. Specifically, we diagnose precipitation minus evaporation (Supplementary Information section  H.5 ) rather than directly predicting these as in machine-learning-based approaches 3 . For short weather forecasts, the mean of precipitation minus evaporation has a realistic spatial distribution that is very close to ERA5 data (Extended Data Fig. 4c–e ). The precipitation-minus-evaporation rate distribution of NeuralGCM-0.7° closely matches the ERA5 distribution in the extratropics (Extended Data Fig. 4b ), although it underestimates extreme events in the tropics (Extended Data Fig. 4a ). It is noted that the current version of NeuralGCM directly predicts tendencies for an atmospheric column, and thus cannot distinguish between precipitation and evaporation.

Geostrophic wind balance

We examined the extent to which NeuralGCM, GraphCast and ECMWF-HRES capture the geostrophic wind balance, the near-equilibrium between the dominant forces that drive large-scale dynamics in the mid-latitudes 30 . A recent study 16 highlighted that Pangu misrepresents the vertical structure of the geostrophic and ageostrophic winds and noted a deterioration at longer lead times. Similarly, we observe that GraphCast shows an error that worsens with lead time. In contrast, NeuralGCM more accurately depicts the vertical structure of the geostrophic and ageostrophic winds, as well as their ratio, compared with GraphCast across various rollouts, when compared against ERA5 data (Extended Data Fig. 3 ). However, ECMWF-HRES still shows a slightly closer alignment to ERA5 data than NeuralGCM does. Within NeuralGCM, the representation of the geostrophic wind’s vertical structure only slightly degrades in the initial few days, showing no noticeable changes thereafter, particularly beyond day 5.

Generalizing to unseen data

Physically consistent weather models should still perform well for weather conditions for which they were not trained. We expect that NeuralGCM may generalize better than machine-learning-only atmospheric models, because NeuralGCM employs neural networks that act locally in space, on individual vertical columns of the atmosphere. To explore this hypothesis, we compare versions of NeuralCGM-0.7° and GraphCast trained to 2017 on 5 years of weather forecasts beyond the training period (2018–2022) in Supplementary Fig. 36 . Unlike GraphCast, NeuralGCM does not show a clear trend of increasing error when initialized further into the future from the training data. To extend this test beyond 5 years, we trained a NeuralGCM-2.8° model using only data before 2000, and tested its skill for over 21 unseen years (Supplementary Fig. 35 ).

Climate simulations

Although our deterministic NeuralGCM models are trained to predict weather up to 3 days ahead, they are generally capable of simulating the atmosphere far beyond medium-range weather timescales. For extended climate simulations, we prescribe historical sea surface temperature (SST) and sea-ice concentration. These simulations feature many emergent phenomena of the atmosphere on timescales from months to decades.

For climate simulations with NeuralGCM, we use 2.8° and 1.4° deterministic models, which are relatively inexpensive to train (Supplementary Information section  G.7 ) and allow us to explore a larger parameter space to find stable models. Previous studies found that running extended simulations with hybrid models is challenging due to numerical instabilities and climate drift 21 . To quantify stability in our selected models, we run multiple initial conditions and report how many of them finish without instability.

Seasonal cycle and emergent phenomena

To assess the capability of NeuralGCM to simulate various aspects of the seasonal cycle, we run 2-year simulations with NeuralGCM-1.4°. for 37 different initial conditions spaced every 10 days for the year 2019. Out of these 37 initial conditions, 35 successfully complete the full 2 years without instability; for case studies of instability, see Supplementary Information section  H.7 , and Supplementary Figs. 26 and 27 . We compare results from NeuralGCM-1.4° for 2020 with ERA5 data and with outputs from the X-SHiELD global cloud-resolving model, which is coupled to an ocean model nudged towards reanalysis 31 . This X-SHiELD run has been used as a target for training machine-learning climate models 24 . For comparison, we evaluate models after regridding predictions to 1.4° resolution. This comparison slightly favours NeuralGCM because NeuralGCM was tuned to match ERA5, but the discrepancy between ERA5 and the actual atmosphere is small relative to model error.

Figure 4a shows the temporal variation of the global mean temperature to 2020, as captured by 35 simulations from NeuralGCM, in comparison with the ERA5 reanalysis and standard climatology benchmarks. The seasonality and variability of the global mean temperature from NeuralGCM are quantitatively similar to those observed in ERA5. The ensemble-mean temperature RMSE for NeuralGCM stands at 0.16 K when benchmarked against ERA5, which is a significant improvement over the climatology’s RMSE of 0.45 K. We find that NeuralGCM accurately simulates the seasonal cycle, as evidenced by metrics such as the annual cycle of the global precipitable water (Supplementary Fig. 30a ) and global total kinetic energy (Supplementary Fig. 30b ). Furthermore, the model captures essential atmospheric dynamics, including the Hadley circulation and the zonal-mean zonal wind (Supplementary Fig. 28 ), as well as the spatial patterns of eddy kinetic energy in different seasons (Supplementary Fig. 31 ), and the distinctive seasonal behaviours of monsoon circulation (Supplementary Fig. 29 ; additional details are provided in Supplementary Information section  I.1 ).

a , Global mean temperature for ERA5 14 (orange), 1990–2019 climatology (black) and NeuralGCM-1.4° (blue) for 2020 using 35 simulations initialized every 10 days during 2019 (thick line, ensemble mean; thin lines, different initial conditions). b , Yearly global mean temperature for ERA5 (orange), mean over 22 CMIP6 AMIP experiments 34 (violet; model details are in Supplementary Information section  I.3 ) and NeuralGCM-2.8° for 22 AMIP-like simulations with prescribed SST initialized every 10 days during 1980 (thick line, ensemble mean; thin lines, different initial conditions). c , The RMSB of the 850-hPa temperature averaged between 1981 and 2014 for 22 NeuralGCM-2.8° AMIP runs (labelled NGCM), 22 CMIP6 AMIP experiments (labelled AMIP) and debiased 22 CMIP6 AMIP experiments (labelled AMIP*; bias was removed by removing the 850-hPa global temperature bias). In the box plots, the red line represents the median. The box delineates the first to third quartiles; the whiskers extend to 1.5 times the interquartile range (Q1 − 1.5IQR and Q3 + 1.5IQR), and outliers are shown as individual dots. d , Vertical profiles of tropical (20° S–20° N) temperature trends for 1981–2014. Orange, ERA5; black dots, Radiosonde Observation Correction using Reanalyses (RAOBCORE) 41 ; blue dots, mean trends for NeuralGCM; purple dots, mean trends from CMIP6 AMIP runs (grey and black whiskers, 25th and 75th percentiles for NeuralGCM and CMIP6 AMIP runs, respectively). e – g , Tropical cyclone tracks for ERA5 ( e ), NeuralGCM-1.4° ( f ) and X-SHiELD 31 ( g ). h – k , Mean precipitable water for ERA5 ( h ) and the precipitable water bias in NeuralGCM-1.4° ( i ), initialized 90 days before mid-January 2020 similarly to X-SHiELD, X-SHiELD ( j ) and climatology ( k ; averaged between 1990 and 2019). In d – i , quantities are calculated between mid-January 2020 and mid-January 2021 and all models were regridded to a 256 × 128 Gaussian grid before computation and tracking.

Next, we compare the annual biases of a single NeuralGCM realization with a single realization of X-SHiELD (the only one available), both initiated in mid-October 2019. We consider 19 January 2020 to 17 January 2021, the time frame for which X-SHiELD data are available. Global cloud-resolving models, such as X-SHiELD, are considered state of the art, especially for simulating the hydrological cycle, owing to their resolution being capable of resolving deep convection 32 . The annual bias in precipitable water for NeuralGCM (RMSE of 1.09 mm) is substantially smaller than the biases of both X-SHiELD (RMSE of 1.74 mm) and climatology (RMSE of 1.36 mm; Fig. 4i–k ). Moreover, NeuralGCM shows a lower temperature bias in the upper and lower troposphere than X-SHiELD (Extended Data Fig. 6 ). We also indirectly compare precipitation bias in X-SHiELD with precipitation-minus-evaporation bias in NeuralGCM-1.4°, which shows slightly larger bias and grid-scale artefacts for NeuralGCM (Extended Data Fig. 5 ).

Finally, to assess the capability of NeuralGCM to generate tropical cyclones in an annual model integration, we use the tropical cyclone tracker TempestExtremes 33 , as described in Supplementary Information section   I.2 , Supplementary Fig. 34 and Supplementary Table 6 . Figure 4e–g shows that NeuralGCM, even at a coarse resolution of 1.4°, produces realistic trajectories and counts of tropical cyclone (83 versus 86 in ERA5 for the corresponding period), whereas X-SHiELD, when regridded to 1.4° resolution, substantially underestimates the tropical cyclone count (40). Additional statistical analyses of tropical cyclones can be found in Extended Data Figs. 7 and 8 .

Decadal simulations

To assess the capability of NeuralGCM to simulate historical temperature trends, we conduct AMIP-like simulations over a duration of 40 years with NeuralGCM-2.8°. Out of 37 different runs with initial conditions spaced every 10 days during the year 1980, 22 simulations were stable for the entire 40-year period, and our analysis focuses on these results. We compare with 22 simulations run with prescribed SST from the Coupled Model Intercomparison Project Phase 6 (CMIP6) 34 , listed in Supplementary Information section  I.3 .

We find that all 40-year simulations of NeuralGCM, as well as the mean of the 22 AMIP runs, accurately capture the global warming trends observed in ERA5 data (Fig. 4b ). There is a strong correlation in the year-to-year temperature trends with ERA5 data, suggesting that NeuralGCM effectively captures the impact of SST forcing on climate. When comparing spatial biases averaged over 1981–2014, we find that all 22 NeuralGCM-2.8° runs have smaller bias than the CMIP6 AMIP runs, and this result remains even when removing the global temperature bias in CMIP6 AMIP runs (Fig. 4c and Supplementary Figs. 32 and 33 ).

Next, we investigated the vertical structure of tropical warming trends, which climate models tend to overestimate in the upper troposphere 35 . As shown in Fig. 4d , the trends, calculated by linear regression, of NeuralGCM are closer to ERA5 than those of AMIP runs. In particular, the bias in the upper troposphere is reduced. However, NeuralGCM does show a wider spread in its predictions than the AMIP runs, even at levels near the surface where temperatures are typically more constrained by prescribed SST.

Lastly, we evaluated NeuralGCM’s capability to generalize to unseen warmer climates by conducting AMIP simulations with increased SST (Supplementary Information section  I.4.2 ). We find that NeuralGCM shows some of the robust features of climate warming response to modest SST increases (+1 K and +2 K); however, for more substantial SST increases (+4 K), NeuralGCM’s response diverges from expectations (Supplementary Fig. 37 ). In addition, AMIP simulations with increased SST show climate drift, underscoring NeuralGCM’s limitations in this context (Supplementary Fig. 38 ).

NeuralGCM is a differentiable hybrid atmospheric model that combines the strengths of traditional GCMs with machine learning for weather forecasting and climate simulation. To our knowledge, NeuralGCM is the first machine-learning-based model to make accurate ensemble weather forecasts, with better CRPS than state-of-the-art physics-based models. It is also, to our knowledge, the first hybrid model that achieves comparable spatial bias to global cloud-resolving models, can simulate realistic tropical cyclone tracks and can run AMIP-like simulations with realistic historical temperature trends. Overall, NeuralGCM demonstrates that incorporating machine learning is a viable alternative to building increasingly detailed physical models 32 for improving GCMs.

Compared with traditional GCMs with similar skill, NeuralGCM is computationally efficient and low complexity. NeuralGCM runs at 8- to 40-times-coarser horizontal resolution than ECMWF’s Integrated Forecasting System and global cloud-resolving models, which enables 3 to 5 orders of magnitude savings in computational resources. For example, NeuralGCM-1.4° simulates 70,000 simulation days in 24 hours using a single tensor-processing-unit versus 19 simulated days on 13,824 central-processing-unit cores with X-SHiELD (Extended Data Table 1 ). This can be leveraged for previously impractical tasks such as large ensemble forecasting. NeuralGCM’s dynamical core uses global spectral methods 36 , and learned physics is parameterized with fully connected neural networks acting on single vertical columns. Substantial headroom exists to pursue higher accuracy using advanced numerical methods and machine-learning architectures.

Our results provide strong evidence for the disputed hypothesis 37 , 38 , 39 that learning to predict short-term weather is an effective way to tune parameterizations for climate. NeuralGCM models trained on 72-hour forecasts are capable of realistic multi-year simulation. When provided with historical SSTs, they capture essential atmospheric dynamics such as seasonal circulation, monsoons and tropical cyclones. However, we will probably need alternative training strategies 38 , 39 to learn important processes for climate with subtle impacts on weather timescales, such as a cloud feedback.

The NeuralGCM approach is compatible with incorporating either more physics or more machine learning, as required for operational weather forecasts and climate simulations. For weather forecasting, we expect that end-to-end learning 40 with observational data will allow for better and more relevant predictions, including key variables such as precipitation. Such models could include neural networks acting as corrections to traditional data assimilation and model diagnostics. For climate projection, NeuralGCM will need to be reformulated to enable coupling with other Earth-system components (for example, ocean and land), and integrating data on the atmospheric chemical composition (for example, greenhouse gases and aerosols). There are also research challenges common to current machine-learning-based climate models 19 , including the capability to simulate unprecedented climates (that is, generalization), adhering to physical constraints, and resolving numerical instabilities and climate drift. NeuralGCM’s flexibility to incorporate physics-based models (for example, radiation) offers a promising avenue to address these challenges.

Models based on physical laws and empirical relationships are ubiquitous in science. We believe the differentiable hybrid modelling approach of NeuralGCM has the potential to transform simulation for a wide range of applications, such as materials discovery, protein folding and multiphysics engineering design.

Differentiable atmospheric model

NeuralGCM combines components of the numerical solver and flexible neural network parameterizations. Simulation in time is carried out in a coordinate system suitable for solving the dynamical equations of the atmosphere, describing large-scale fluid motion and thermodynamics under the influence of gravity and the Coriolis force.

Our differentiable dynamical core is implemented in JAX, a library for high-performance code in Python that supports automatic differentiation 42 . The dynamical core solves the hydrostatic primitive equations with moisture, using a horizontal pseudo-spectral discretization and vertical sigma coordinates 36 , 43 . We evolve seven prognostic variables: vorticity and divergence of horizontal wind, temperature, surface pressure, and three water species (specific humidity, and specific ice and liquid cloud water content).

Our learned physics module uses the single-column approach of GCMs 2 , whereby information from only a single atmospheric column is used to predict the impact of unresolved processes occurring within that column. These effects are predicted using a fully connected neural network with residual connections, with weights shared across all atmospheric columns (Supplementary Information section  C.4 ).

The inputs to the neural network include the prognostic variables in the atmospheric column, total incident solar radiation, sea-ice concentration and SST (Supplementary Information section  C.1 ). We also provide horizontal gradients of the prognostic variables, which we found improves performance 44 . All inputs are standardized to have zero mean and unit variance using statistics precomputed during model initialization. The outputs are the prognostic variable tendencies scaled by the fixed unconditional standard deviation of the target field (Supplementary Information section  C.5 ).

To interface between ERA5 14 data stored in pressure coordinates and the sigma coordinate system of our dynamical core, we introduce encoder and decoder components (Supplementary Information section  D ). These components perform linear interpolation between pressure levels and sigma coordinate levels. We additionally introduce learned corrections to both encoder and decoder steps (Supplementary Figs. 4–6 ), using the same column-based neural network architecture as the learned physics module. Importantly, the encoder enables us to eliminate the gravity waves from initialization shock 45 , which otherwise contaminate forecasts.

Figure 1a shows the sequence of steps that NeuralGCM takes to make a forecast. First, it encodes ERA5 data at t  =  t 0 on pressure levels to initial conditions on sigma coordinates. To perform a time step, the dynamical core and learned physics (Fig. 1b ) then compute tendencies, which are integrated in time using an implicit–explicit ordinary differential equation solver 46 (Supplementary Information section  E and Supplementary Table 2 ). This is repeated to advance the model from t  =  t 0 to t  =  t final . Finally, the decoder converts predictions back to pressure levels.

The time-step size of the ODE solver (Supplementary Table 3 ) is limited by the Courant–Friedrichs–Lewy condition on dynamics, and can be small relative to the timescale of atmospheric change. Evaluating learned physics is approximately 1.5 times as expensive as a time step of the dynamical core. Accordingly, following the typical practice for GCMs, we hold learned physics tendencies constant for multiple ODE time steps to reduce computational expense, typically corresponding to 30 minutes of simulation time.

Deterministic and stochastic models

We train deterministic NeuralGCM models using a combination of three loss functions (Supplementary Information section  G.4 ) to encourage accuracy and sharpness while penalizing bias. During the main training phase, all losses are defined in a spherical harmonics basis. We use a standard mean squared error loss for prompting accuracy, modified to progressively filter out contributions from higher total wavenumbers at longer lead times (Supplementary Fig. 8 ). This filtering approach tackles the ‘double penalty problem’ 47 as it prevents the model from being penalized for predicting high-wavenumber features in incorrect locations at later times, especially beyond the predictability horizon. A second loss term encourages the spectrum to match the training data using squared loss on the total wavenumber spectrum of prognostic variables. These first two losses are evaluated on both sigma and pressure levels. Finally, a third loss term discourages bias by adding mean squared error on the batch-averaged mean amplitude of each spherical harmonic coefficient. For analysis of the impact that various loss functions have, refer to Supplementary Information section  H.6.1 , and Supplementary Figs. 23 and 24 . The combined action of the three training losses allow the resulting models trained on 3-day rollouts to remain stable during years-to-decades-long climate simulations. Before final evaluations, we perform additional fine-tuning of just the decoder component on short rollouts of 24 hours (Supplementary Information section  G.5 ).

Stochastic NeuralGCM models incorporate inherent randomness in the form of additional random fields passed as inputs to neural network components. Our stochastic loss is based on the CRPS 28 , 48 , 49 . CRPS consists of mean absolute error that encourages accuracy, balanced by a similar term that encourages ensemble spread. For each variable we use a sum of CRPS in grid space and CRPS in the spherical harmonic basis below a maximum cut-off wavenumber (Supplementary Information section  G.6 ). We compute CRPS on rollout lengths from 6 hours to 5 days. As illustrated in Fig. 1 , we inject noise to the learned encoder and the learned physics module by sampling from Gaussian random fields with learned spatial and temporal correlation (Supplementary Information section  C.2 and Supplementary Fig. 2 ). For training, we generate two ensemble members per forecast, which suffices for an unbiased estimate of CRPS.

Data availability

For training and evaluating the NeuralGCM models, we used the publicly available ERA5 dataset 14 , originally downloaded from https://cds.climate.copernicus.eu/ and available via Google Cloud Storage in Zarr format at gs://gcp-public-data-arco-era5/ar/full_37-1h-0p25deg-chunk-1.zarr-v3. To compare NeuralGCM with operational and data-driven weather models, we used forecast datasets distributed as part of WeatherBench2 12 at https://weatherbench2.readthedocs.io/en/latest/data-guide.html , to which we have added NeuralGCM forecasts for 2020. To compare NeuralGCM with atmospheric models in climate settings, we used CMIP6 data available at https://catalog.pangeo.io/browse/master/climate/ , as well as X-SHiELD 24 outputs available on Google Cloud storage in a ‘requester pays’ bucket at gs://ai2cm-public-requester-pays/C3072-to-C384-res-diagnostics. The Radiosonde Observation Correction using Reanalyses (RAOBCORE) V1.9 that was used as reference tropical temperature trends was downloaded from https://webdata.wolke.img.univie.ac.at/haimberger/v1.9/ . Base maps use freely available data from https://www.naturalearthdata.com/downloads/ .

Code availability

The NeuralGCM code base is separated into two open source projects: Dinosaur and NeuralGCM, both publicly available on GitHub at https://github.com/google-research/dinosaur (ref. 50 ) and https://github.com/google-research/neuralgcm (ref. 51 ). The Dinosaur package implements a differentiable dynamical core used by NeuralGCM, whereas the NeuralGCM package provides machine-learning models and checkpoints of trained models. Evaluation code for NeuralGCM weather forecasts is included in WeatherBench2 12 , available at https://github.com/google-research/weatherbench2 (ref. 52 ).

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Acknowledgements

We thank A. Kwa, A. Merose and K. Shah for assistance with data acquisition and handling; L. Zepeda-Núñez for feedback on the paper; and J. Anderson, C. Van Arsdale, R. Chemke, G. Dresdner, J. Gilmer, J. Hickey, N. Lutsko, G. Nearing, A. Paszke, J. Platt, S. Ponda, M. Pritchard, D. Rothenberg, F. Sha, T. Schneider and O. Voicu for discussions.

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These authors contributed equally: Dmitrii Kochkov, Janni Yuval, Ian Langmore, Peter Norgaard, Jamie Smith, Stephan Hoyer

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Google Research, Mountain View, CA, USA

Dmitrii Kochkov, Janni Yuval, Ian Langmore, Peter Norgaard, Jamie Smith, Griffin Mooers, James Lottes, Stephan Rasp, Michael P. Brenner & Stephan Hoyer

Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

Milan Klöwer

European Centre for Medium-Range Weather Forecasts, Reading, UK

Peter Düben & Sam Hatfield

Google DeepMind, London, UK

Peter Battaglia, Alvaro Sanchez-Gonzalez & Matthew Willson

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

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Contributions

D.K., J.Y., I.L., P.N., J.S. and S. Hoyer contributed equally to this work. D.K., J.Y., I.L., P.N., J.S., G.M., J.L. and S. Hoyer wrote the code. D.K., J.Y., I.L., P.N., G.M. and S. Hoyer trained models and analysed the data. M.P.B. and S. Hoyer managed and oversaw the research project. M.K., S.R., P.D., S. Hatfield, P.B. and M.P.B. contributed technical advice and ideas. M.W. ran experiments with GraphCast for comparison with NeuralGCM. A.S.-G. assisted with data preparation. D.K., J.Y., I.L., P.N. and S. Hoyer wrote the paper. All authors gave feedback and contributed to editing the paper.

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Correspondence to Dmitrii Kochkov , Janni Yuval or Stephan Hoyer .

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D.K., J.Y., I.L., P.N., J.S., J.L., S.R., P.B., A.S.-G., M.W., M.P.B. and S. Hoyer are employees of Google. S. Hoyer, D.K., I.L., J.Y., G.M., P.N., J.S. and M.B. have filed international patent application PCT/US2023/035420 in the name of Google LLC, currently pending, relating to neural general circulation models.

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Extended data figures and tables

Extended data fig. 1 maps of bias for neuralgcm-ens and ecmwf-ens forecasts..

Bias is averaged over all forecasts initialized in 2020.

Extended Data Fig. 2 Maps of spread-skill ratio for NeuralGCM-ENS and ECMWF-ENS forecasts.

Spread-skill ratio is averaged over all forecasts initialized in 2020.

Extended Data Fig. 3 Geostrophic balance in NeuralGCM, GraphCast 3 and ECMWF-HRES.

Vertical profiles of the extratropical intensity (averaged between latitude 30°–70° in both hemispheres) and over all forecasts initialized in 2020 of (a,d,g) geostrophic wind, (b,e,h) ageostrophic wind and (c,f,i) the ratio of the intensity of ageostrophic wind over geostrophic wind for ERA5 (black continuous line in all panels), (a,b,c) NeuralGCM-0.7°, (d,e,f) GraphCast and (g,h,i) ECMWF-HRES at lead times of 1 day, 5 days and 10 days.

Extended Data Fig. 4 Precipitation minus evaporation calculated from the third day of weather forecasts.

(a) Tropical (latitudes −20° to 20°) precipitation minus evaporation (P minus E) rate distribution, (b) Extratropical (latitudes 30° to 70° in both hemispheres) P minus E, (c) mean P minus E for 2020 ERA5 14 and (d) NeuralGCM-0.7° (calculated from the third day of forecasts and averaged over all forecasts initialized in 2020), (e) the bias between NeuralGCM-0.7° and ERA5, (f-g) Snapshot of daily precipitation minus evaporation for 2020-01-04 for (f) NeuralGCM-0.7° (forecast initialized on 2020-01-02) and (g) ERA5.

Extended Data Fig. 5 Indirect comparison between precipitation bias in X-SHiELD and precipitation minus evaporation bias in NeuralGCM-1.4°.

Mean precipitation calculated between 2020-01-19 and 2021-01-17 for (a) ERA5 14 (c) X-SHiELD 31 and the biases in (e) X-SHiELD and (g) climatology (ERA5 data averaged over 1990-2019). Mean precipitation minus evaporation calculated between 2020-01-19 and 2021-01-17 for (b) ERA5 (d) NeuralGCM-1.4° (initialized in October 18th 2019) and the biases in (f) NeuralGCM-1.4° and (h) climatology (data averaged over 1990–2019).

Extended Data Fig. 6 Yearly temperature bias for NeuralGCM and X-SHiELD 31 .

Mean temperature between 2020-01-19 to 2020-01-17 for (a) ERA5 at 200hPa and (b) 850hPa. (c,d) the bias in the temperature for NeuralGCM-1.4°, (e,f) the bias in X-SHiELD and (g,h) the bias in climatology (calculated from 1990–2019). NeuralGCM-1.4° was initialized in 18th of October (similar to X-SHiELD).

Extended Data Fig. 7 Tropical Cyclone densities and annual regional counts.

(a) Tropical Cyclone (TC) density from ERA5 14 data spanning 1987–2020. (b) TC density from NeuralGCM-1.4° for 2020, generated using 34 different initial conditions all initialized in 2019. (c) Box plot depicting the annual number of TCs across different regions, based on ERA5 data (1987–2020), NeuralGCM-1.4° for 2020 (34 initial conditions), and orange markers show ERA5 for 2020. In the box plots, the red line represents the median; the box delineates the first to third quartiles; the whiskers extend to 1.5 times the interquartile range (Q1 − 1.5IQR and Q3 + 1.5IQR), and outliers are shown as individual dots. Each year is defined from January 19th to January 17th of the following year, aligning with data availability from X-SHiELD. For NeuralGCM simulations, the 3 initial conditions starting in January 2019 exclude data for January 17th, 2021, as these runs spanned only two years.

Extended Data Fig. 8 Tropical Cyclone maximum wind distribution in NeuralGCM vs. ERA5 14 .

Number of Tropical Cyclones (TCs) as a function of maximum wind speed at 850hPa across different regions, based on ERA5 data (1987–2020; in orange), and NeuralGCM-1.4° for 2020 (34 initial conditions; in blue). Each year is defined from January 19th to January 17th of the following year, aligning with data availability from X-SHiELD. For NeuralGCM simulations, the 3 initial conditions starting in January 2019 exclude data for January 17th, 2021, as these runs spanned only two years.

Supplementary information

Supplementary information.

Supplementary Information (38 figures, 6 tables): (A) Lines of code in atmospheric models; (B) Dynamical core of NeuralGCM; (C) Learned physics of NeuralGCM; (D) Encoder and decoder of NeuralGCM; (E) Time integration; (F) Evaluation metrics; (G) Training; (H) Additional weather evaluations; (I) Additional climate evaluations.

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Kochkov, D., Yuval, J., Langmore, I. et al. Neural general circulation models for weather and climate. Nature 632 , 1060–1066 (2024). https://doi.org/10.1038/s41586-024-07744-y

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