Deep Learning in Deterministic Computational Mechanics

Abstract

The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning -- instead, the primary audience is researchers at the verge of entering this field or those who attempt to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.

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• Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices

Cited by in corpus (11)

• Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning
• Neural Networks for Generating Better Local Optima in Topology Optimization
• I-FENN with Temporal Convolutional Networks: expediting the load-history analysis of non-local gradient damage propagation
• Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network
• Experimental Learning of a Hyperelastic Behavior with a Physics-Augmented Neural Network
• A hybrid electromechanical phase-field and deep learning framework for predicting fracture in dielectric nanocomposites
• Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks
• Data Publishing in Mechanics and Dynamics: Challenges, Guidelines, and Examples from Engineering Design
• A Memory Efficient Adjoint Method to Enable Billion Parameter Optimization on a Single GPU in Dynamic Problems
• Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables
• Trustworthy AI-based crack-tip segmentation using domain-guided explanations