Machine Learning in Geomechanics 2

Preface ix
Ioannis STEFANOU and Felix DARVE

Chapter 1. Data-Driven Modeling in Geomechanics .. 1
Konstantinos KARAPIPERIS

1.1. Introduction 2

1.2. Data-driven computational mechanics 3

1.2.1. Cauchy continuum – elasticity 3

1.2.2. Micropolar continuum – elasticity 6

1.2.3. Extension to inelasticity 10

1.2.4. Data sampling 11

1.3. Applications 15

1.4. Conclusions 17

1.5. References 17

Chapter 2 Bayesian Inference in Geomechanics 25
Dhruv V. PATEL, Jonghyun “Harry” LEE, Peter K. KITANIDIS and Eric F. DARVE

2.1. Introduction 26

2.2. Inverse problems 26

2.2.1. Regularization methods 28

2.2.2. Bayesian inversion 30

2.3. Machine learning-assisted Bayesian inference 33

2.3.1. Informative and accurate prior characterization with deep generative modeling 34

2.3.2. Computationally inexpensive likelihood evaluation with operator learning 40

2.3.3. Efficient posterior inference in a black-box setting 44

2.4. Conclusion 49

2.5. References 50

Chapter 3 Physics-Informed and Thermodynamics-Based Neural Networks 57
Filippo MASI and Ioannis STEFANOU

3.1. Introduction 58

3.2. Physics-informed neural networks 60

3.2.1. Methodology 61

3.2.2. Hands-on example 63

3.3. Thermodynamics-based neural networks 68

3.3.1. Theoretical framework 70

3.3.2. Methodology 75

3.3.3. Digital twins of granular materials: a pedagogic example 80

3.3.4. Speed up multiscale simulations 87

3.4. Conclusions 93

3.5. Acknowledgments 95

3.6. References 95

Chapter 4 Introduction to Reinforcement Learning with Applications in Geomechanics 101
Alexandros STATHAS, Diego GUTIERREZ-ORIBIO and Ioannis STEFANOU

4.1. Introduction 102

4.2. Reinforcement learning: the basics 106

4.2.1. Basic definitions: deterministic case 106

4.2.2. Probabilistic environment and stochastic policies 120

4.2.3. Function approximation 146

4.2.4. Summing up 153

4.2.5. AC Network 155

4.3. Applications to geomechanics 156

4.3.1. Control theory: the basics 156

4.3.2. Reduced model for earthquakes: the spring-slider 159

4.3.3. Controlling induced seismicity in a geothermal reservoir 171

4.4. Conclusions 178

4.5. Acknowledgment 180

4.6. References 180

Chapter 5 Artificial Neural Networks: Basic Architectures and Training Strategies 185
Filippo GATTI

5.1. Neural networks 187

5.1.1. The artificial neuron 187

5.1.2. The multi-layer perceptron 191

5.1.3. Why MLP? 196

5.1.4. How to improve the MLP accuracy? 208

5.1.5. From neurons to filters 211

5.1.6. Deep convolutional architectures 227

5.1.7. Time-forward prediction 233

5.1.8. Recurrent neural networks 234

5.1.9. Long-short term memory 240

5.2. Automatic differentiation 243

5.2.1. Updating weights with the chain rule 244

5.2.2. Effective backward propagation 247

5.2.3. Countermeasures to vanishing gradients 255

5.2.4. Back-propagation through time 265

5.3. References 269

List of Authors 277

Index 279

Summary of Volume 1 283