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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.
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.
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