Deep Learning in Computational Mechanics
An Introductory Course
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The Finite Cell Method for Simulation of Additive Manufacturing
Additive manufacturing processes are driven by moving laser-induced thermal sources which induce strong heat fluxes and fronts of phase change coupled to mechanical fields. Their numerical simulation poses sev...
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Article
Open AccessA Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics
In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures a...
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Machine Learning in Physics and Engineering
Machine Learning is already being frequently used in computer vision, recommendation systems, medical diagnosis, or financial forecasting. Recently, physics and engineering have also taken advantage of machine...
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Deep Energy Method
The deep energy method is an alternative to the physics-informed neural networks (PINNs). Both approaches leverage the underlying physics to reduce the amount of data required. Instead of directly using the go...
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Introduction
Significant advancements have been made in the field of artificial intelligence in recent years. Thus, artificial intelligence has also become of greater interest in areas other than computer science, such as ...
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Fundamental Concepts of Machine Learning
Machine Learning algorithms are different from conventional algorithms as they automatically improve through experience. They traditionally accomplish this using data. This chapter gives an overview of the fun...
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Neural Networks
Artificial neural networks (ANNs) are state-of-the-art machine learning architectures modeling neurons and their connections through weights and biases. ANNs serve as universal function approximators, meaning ...
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Physics-Informed Neural Networks
Physics-informed neural networks (PINNs) are used for problems where data are scarce. The underlying physics is enforced via the governing differential equation, including the residual in the cost function. PI...
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Article
Hierarchically refined isogeometric analysis of trimmed shells
This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff–Love shells. To cope with these issues and to r...
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Article
Open AccessMulti-level hp-adaptivity and explicit error estimation
Recently, a multi-level hp-version of the finite element method (FEM) was proposed to ease the difficulties of treating hanging nodes, while providing full hp-approximation capabilities. In the original paper, th...
