Deep Learning in Computational Mechanics: An Introductory Course

Description

This book provides a first course on deep learning in computational mechanics. The book starts with a short introduction to machine learning's fundamental concepts before neural networks are explained thoroughly. It then provides an overview of current topics in physics and engineering, setting the stage for the book's main topics: physics-informed neural networks and the deep energy method. The idea of the book is to provide the basic concepts in a mathematically sound manner and yet to stay as simple as possible. To achieve this goal, mostly one-dimensional examples are investigated, such as approximating functions by neural networks or the simulation of the temperature's evolution in a one-dimensional bar. Each chapter contains examples and exercises which are either solved analytically or in PyTorch, an open-source machine learning framework for python. Contents 1 Introduction References 2 Fundamental Concepts of Machine Learning 2.1 Definition 2.2 Data Structure 2.3 Types of Learning 2.3.1 Supervised Learning 2.3.2 Unsupervised Learning 2.3.3 Semi-supervised Learning 2.3.4 Reinforcement Learning 2.4 Machine Learning Tasks 2.4.1 Regression 2.4.2 Classification 2.4.3 Clustering 2.5 Example: Linear Regression 2.6 Optimization Techniques 2.7 Overfitting Versus Underfitting 2.8 Regularization References 3 Neural Networks 3.1 Feed-Forward Neural Network 3.2 Forward Propagation 3.3 Differentiation 3.4 Backpropagation 3.5 Activation Function 3.6 Learning Algorithm 3.7 Regularization of Neural Networks 3.7.1 Early Stopping 3.7.2 L1 and L2 Regularization 3.7.3 Dropout 3.7.4 Dataset Augmentation 3.8 Example: Approximating the Sine Function 3.9 Input Derivatives 3.10 Advanced Architectures 3.10.1 Convolutional Neural Network 3.10.2 Recurrent Neural Network References 4 Machine Learning in Physics and Engineering 4.1 General Reviews 4.2 Combined Methods 4.3 Surrogate Models References 5 Physics-Informed Neural Networks 5.1 Overview 5.2 Data-Driven Inference 5.2.1 Static Model 5.2.2 Continuous-Time Model 5.2.3 Discrete-Time Model 5.3 Data-Driven Identification 5.3.1 Static Model 5.4 Related Work References 6 Deep Energy Method 6.1 Static Model References Appendix A Exercises Appendix B Additional Figures B.1 Section 5.2.2摥映數爠eflinkssec:ContinuousInference5.2.25 Index