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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.
Fundamental Concepts of Machine Learning
Neural Networks
Machine Learning in Physics and Engineering
Physics-Informed Neural Networks
Deep Energy Method
Appendixes
Exercises
Additional Figures