This repository includes the codes and Jupyter notebooks that were written for the 2023 Alert Geomaterials doctoral school on "Machine Learning in Geomechanics".
See program.
The volume is organized in ten chapters:
The first chapter, “Overview of Machine Learning”, is the introductory chapter of this volume. In this chapter we explain how the machine can learn, we show a classification of the main methods in Machine Learning, we outline some applications of ML in Geomechanics and we highlight its limitations.
The second chapter, “Introduction to regression methods”, focuses on regression, which is one of the fundamental pillars of supervised Machine Learning. In this chapter we introduce the essential concepts in regression analysis and methods, by providing hands-on, practical examples.
The target of the third chapter, “Unsupervised Learning: Basic Concepts and Application to Particle Dynamics”, is twofold. The first part of this chapter is devoted to the description of the basic concepts of the most popular techniques of unsupervised learning. The second part illustrates an application of unsupervised learning to the discovery of patterns in particles dynamics.
The fourth chapter, “Classification Techniques in Machine Learning”, aims at describing what the problem of classification in Machine Learning is and illustrates some of the methods used for solving it, without resorting to Artificial Neural Networks. Hands-on examples are given and Active Learning is discussed.
Chapter five, “Data-Driven Modeling in Geomechanics”, presents the theoretical framework of the so called data-driven computational mechanics. Furthermore, it shows some of its applications for the solution of problems involving Cauchy and Cosserat continua with elastic and inelastic materials, which, naturally, represent common descriptions of geomaterials.
The sixth chapter, “Non-Euclidean machine learning for geomechanics”, is intended to provide a concise review on how to train, verify and validate constitutive models enhanced by graph-theoretic data. The use of graph convolutional neural networks for constitutive modeling, material design, and the solution of inverse problems is discussed.
The next two chapters, “Artificial Neural Networks: layer architectures, optimizers and automatic differentiation” and “Artificial Neural Networks: advanced topics” provide a comprehensive introduction to Artificial Neural Networks (ANN). Several hands-on examples are given to help the reader grasp the main ideas and tools of the most important ANN architectures. More advanced topics are also discussed and the connection of ANN with information theory is made.
Chapter nine “Physics-informed and thermodynamics-based neural networks” shows how to inject prior knowledge into deep learning algorithms. Using various examples, we present Physics-Informed Neural Networks for the discovery of partial differential equations and Thermodynamics-based Artificial Neural Networks for the discovery of constitutive models of complex, inelastic materials.
The last chapter, “Introduction to Reinforcement Learning with Applications in Geomechanics”, presents the basic concepts of Reinforcement Learning, which enables the development of software agents that are capable of making optimal decisions in dynamic and uncertain environments. The chapter closes with two applications of Reinforcement Learning in Geomechanics.
All the hands-on exercises of the chapters can be found here.
All the hands-on exercises of the lectures can be found here.