Intro
Preface
Contents
About the Editors
1 Machine Learning in Computer Aided Engineering
1.1 Introduction
1.2 Machine Learning Procedures Employed in CAE
1.2.1 Machine Learning Aspects and Classification of Procedures
1.2.2 Overview of Classical Machine Learning Procedures Used in CAE
1.3 Constraining to, and Incorporating Physics in, Data-Driven Methods
1.3.1 Incorporating Physics in, and Learning Physics From, the Dataset
1.3.2 Incorporating Physics in the Design of a ML Method
1.3.3 Data Assimilation and Correction Methods

1.3.4 ML Methods Designed to Learn Physics
1.4 Applications of Machine Learning in Computer Aided Engineering
1.4.1 Constitutive Modeling and Multiscale Applications
1.4.2 Fluid Mechanics Applications
1.4.3 Structural Mechanics Applications
1.4.4 Machine Learning Approaches Motivated in Structural Mechanics and by Finite Element Concepts
1.4.5 Multiphysics Problems
1.4.6 Machine Learning in Manufacturing and Design
1.5 Conclusions
References
2 Artificial Neural Networks
2.1 Introduction
2.2 Biological Motivation and Pre-history
2.2.1 Memory

2.2.2 Learning
2.2.3 Parallel Distributed Processing Paradigm
2.2.4 The Artificial Neuron
2.2.5 The Perceptron
2.3 The First Age-The Multi-layer Perceptron
2.3.1 Existence of Solutions
2.3.2 Uniqueness of Solutions
2.3.3 Generalization and Regularization
2.3.4 Choice of Output Activations Functions
2.4 A First-Age Case Study: Structural Monitoring of an Aircraft Wing
2.5 The Second Age-Deep Learning
2.5.1 Convolutional Neural Networks (CNNs)
2.5.2 A Little More History
2.5.3 Other Recent Developments
2.6 Conclusions
References
3 Gaussian Processes

3.1 Introduction
3.1.1 A Visual Introduction To Gaussian Processes
3.1.2 Gaussian Process Regression
3.1.3 Implementation and Learning of the GP
3.2 Beyond the Gaussian Process
3.2.1 Large Training Data
3.2.2 Non-Gaussian Likelihoods
3.2.3 Multiple-Output GPs
3.3 A Case Study with Wind Turbine Power Curves
3.4 Conclusions
References
4 Machine Learning Methods for Constructing Dynamic Models From Data
4.1 Introduction
4.2 Modeling Viewpoints
4.3 Learning Paradigms: Burgers' Equation
4.4 Dynamic Models From Data
4.4.1 Dynamic Mode Decomposition

4.4.2 Sparse Identification of Nonlinear Dynamics
4.4.3 Neural Networks
4.5 Joint Discovery of Coordinates and Models
4.6 Conclusions
References
5 Physics-Informed Neural Networks: Theory and Applications
5.1 Introduction
5.2 Basics of Artificial Neural Networks
5.2.1 Feed-Forward Neural Networks
5.2.2 Activation Functions
5.2.3 Training
5.2.4 Testing and Validation
5.2.5 Optimizers
5.3 Physics-Informed Neural Networks
5.3.1 Collocation Method
5.3.2 Energy Minimization Method
5.4 Numerical Applications
5.4.1 Forward Problems