Machine Learning in Geomechanics 2

Ioannis Stefanou is Professor at ECN, France, and leads several geomechanics projects. His main research interests include mechanics, geomechanics, control, induced seismicity and machine learning.Félix Darve is Emeritus Professor at the Soils Solids Structures Risks (3SR) laboratory, Grenoble-INP, Grenoble Alpes University, France. His research focuses on computational geomechanics.

• Preface ixIoannis STEFANOU and Félix DARVEChapter 1. Data-Driven Modeling in Geomechanics .. 1Konstantinos KARAPIPERIS1.1. Introduction 21.2. Data-driven computational mechanics 31.2.1. Cauchy continuum – elasticity 31.2.2. Micropolar continuum – elasticity 61.2.3. Extension to inelasticity 101.2.4. Data sampling 111.3. Applications 151.4. Conclusions 171.5. References 17Chapter 2 Bayesian Inference in Geomechanics 25Dhruv V. PATEL, Jonghyun “Harry” LEE, Peter K. KITANIDIS and Eric F. DARVE2.1. Introduction 262.2. Inverse problems 262.2.1. Regularization methods 282.2.2. Bayesian inversion 302.3. Machine learning-assisted Bayesian inference 332.3.1. Informative and accurate prior characterization with deep generative modeling 342.3.2. Computationally inexpensive likelihood evaluation with operator learning 402.3.3. Efficient posterior inference in a black-box setting 442.4. Conclusion 492.5. References 50Chapter 3 Physics-Informed and Thermodynamics-Based Neural Networks 57Filippo MASI and Ioannis STEFANOU3.1. Introduction 583.2. Physics-informed neural networks 603.2.1. Methodology 613.2.2. Hands-on example 633.3. Thermodynamics-based neural networks 683.3.1. Theoretical framework 703.3.2. Methodology 753.3.3. Digital twins of granular materials: a pedagogic example 803.3.4. Speed up multiscale simulations 873.4. Conclusions 933.5. Acknowledgments 953.6. References 95Chapter 4 Introduction to Reinforcement Learning with Applications in Geomechanics 101Alexandros STATHAS, Diego GUTIÉRREZ-ORIBIO and Ioannis STEFANOU4.1. Introduction 1024.2. Reinforcement learning: the basics 1064.2.1. Basic definitions: deterministic case 1064.2.2. Probabilistic environment and stochastic policies 1204.2.3. Function approximation 1464.2.4. Summing up 1534.2.5. AC Network 1554.3. Applications to geomechanics 1564.3.1. Control theory: the basics 1564.3.2. Reduced model for earthquakes: the spring-slider 1594.3.3. Controlling induced seismicity in a geothermal reservoir 1714.4. Conclusions 1784.5. Acknowledgment 1804.6. References 180Chapter 5 Artificial Neural Networks: Basic Architectures and Training Strategies 185Filippo GATTI5.1. Neural networks 1875.1.1. The artificial neuron 1875.1.2. The multi-layer perceptron 1915.1.3. Why MLP? 1965.1.4. How to improve the MLP accuracy? 2085.1.5. From neurons to filters 2115.1.6. Deep convolutional architectures 2275.1.7. Time-forward prediction 2335.1.8. Recurrent neural networks 2345.1.9. Long-short term memory 2405.2. Automatic differentiation 2435.2.1. Updating weights with the chain rule 2445.2.2. Effective backward propagation 2475.2.3. Countermeasures to vanishing gradients 2555.2.4. Back-propagation through time 2655.3. References 269List of Authors 277Index 279Summary of Volume 1 283