The chapter provides a partial overview of machine learning methods and their historical development.

The chapter shows how regularization and preconditioners can be used to alleviate problems with ill-conditioning and inconsistency.

This chapter introduces the conjugate gradient method and some ad hoc methods developed by the machine learning community.

This chapter presents the theory and practice of solving classification and regression problems by a neural network using nonlinear activation functions such as the sigmoid function.

This chapter presents several examples where a fully connected neural network (FCNN) or a support vector machine method is used to process geophysical data.

The recursive equations for both the feed-forward and backward-propagation operations are derived for a multilayered fully connected neural network (FCNN). The workflow and MATLAB pseudocodes are presented for implementing the multilayer neural network algorithm.

This chapter presents the theory and applications of support vector machines.

This chapter presents the fundamentals of the convolution operation and the related operation of correlation.

The theory and practice of convolutional neural networks (CNNs) are introduced where the dense matrices of a fully connected neural network (FCNN) are replaced by the sparse correlation matrices.

This chapter describes several tasks of computer vision for identifying objects in images: image classification, classification+localization, object detection, semantic segmentation, and instance segmentation.

This chapter discusses a modified version of the U-Net architecture for semantic segmentation used to identify and label cracks in photos of sandstone massifs.

This chapter presents the theory of RNN, where the theory of easy-to-understand vanilla RNN (VRNN) is presented first and then followed by the theories of the more practical long short-term memory networks (LSTM) and gated recurrent units (GRUs). The last section presents practical examples of RNN applied to geoscience problems.

This chapter explains the self-attention concept and describes its use in transformer architecture.

This chapter describes practical uses of autoencoders, their theory, problems, regularization, and numerical examples.

This chapter discusses how the convolutional sparse coding method can be used to eliminate both coherent and random noise in seismic data.

The increasing number of large multidimensional data sets being recorded creates challenges for the geoscientists tasked with interpreting them. To mitigate the difficulty of the task, principal component analysis (PCA) is used as an unsupervised machine learning method to compress data to a smaller dimension with minimal information loss.

Clustering algorithms are unsupervised learning methods that avoid the cost of supervised labeling of large sets. This chapter discusses the k-means cluster method, in addition to density-based spatial clustering (DBSCAN) and support vector clustering.

This chapter includes discussion of the mathematical formulation of a GAN and a pseudocode for its implementation. Numerical examples of applying GANs to seismic data are provided, and a summary concludes this chapter.

This chapter presents the more sophisticated sampling methods that are used to sample multivariate probability distributions.

This chapter provides the intuitive meaning of Bayes' theorem and uses examples to describe how it can be applied to geoscience data to produce the most probable earth model and uncertainty estimates of its model parameters. It also shows how the Bayesian maximum a posterior (MAP) estimate of the model parameter vector m is equivalent to the least squares estimate of m with regularization. Finally, Bayes' theorem is applied to satellite images of an oil spill, vertical seismic profile (VSP) data, well-log data, and seismic data to estimate the most probable geophysical parameters subject to constraints.