Deep Learning in Computational Mechanics

This book provides a first course without requiring prerequisite knowledge. Fundamental concepts of machine learning are introduced before explaining neural networks. With this knowledge, prominent topics in deep learning for simulation are explored. These include surrogate modeling, physics-informed neural networks, generative artificial intelligence, Hamiltonian/Lagrangian neural networks, input convex neural networks, and more general machine learning techniques. The idea of the book is to provide basic concepts as simple as possible but in a mathematically sound manner. Starting point are one-dimensional examples including elasticity, plasticity, heat evolution, or wave propagation. The concepts are then expanded to state-of-the-art applications in material modeling, generative artificial intelligence, topology optimization, defect detection, and inverse problems.