Open Access
REVIEW
Deep Learning Applied to Computational Mechanics: A Comprehensive Review, State of the Art, and the Classics
Loc Vu-Quoc1,*, Alexander Humer2
1 Aerospace Engineering, University of Illinois at Urbana-Champaign, Champaign, IL 61801, USA
2 Institute of Technical Mechanics, Johannes Kepler University, Linz, A-4040, Austria
* Corresponding Author: Loc Vu-Quoc. Email:
Computer Modeling in Engineering & Sciences 2023, 137(2), 1069-1343. https://doi.org/10.32604/cmes.2023.028130
Received 01 December 2022; Accepted 01 March 2023; Issue published 26 June 2023
Abstract
Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image,
protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly
deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology)
are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods
combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate
the simulation by predicting certain components in the traditional integration methods. Here, methods (1) and
(2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3) relying on convolutional neural
networks.. Pure ML methods to solve (nonlinear) PDEs are represented by Physics-Informed Neural network
(PINN) methods, which could be combined with attention mechanism to address discontinuous solutions. Both
LSTM and attention architectures, together with modern and generalized classic optimizers to include stochasticity for DL networks, are extensively reviewed. Kernel machines, including Gaussian processes, are provided
to sufficient depth for more advanced works such as shallow networks with infinite width. Not only addressing
experts, readers are assumed familiar with computational mechanics, but not with DL, whose concepts and applications are built up from the basics, aiming at bringing first-time learners quickly to the forefront of research.
History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics, even in well-known references. Positioning and pointing control of a
large-deformable beam is given as an example.
Keywords
Deep learning, breakthroughs, network architectures, backpropagation, stochastic optimization methods from classic to modern, recurrent neural networks, long short-term memory, gated recurrent unit, attention, transformer, kernel machines, Gaussian processes, libraries, Physics-Informed Neural Networks, state-of-the-art, history, limitations, challenges;
Applications to computational mechanics;
Finite-element matrix integration, improved Gauss quadrature;
Multiscale geomechanics, fluid-filled porous media;
Fluid mechanics, turbulence, proper orthogonal decomposition;
Nonlinear-manifold model-order reduction, autoencoder, hyper-reduction using gappy data;
control of large deformable beam
Cite This Article
Vu-Quoc, L., Humer, A. (2023). Deep Learning Applied to Computational Mechanics: A Comprehensive Review, State of the Art, and the Classics.
CMES-Computer Modeling in Engineering & Sciences, 137(2), 1069–1343.