TY - EJOU
AU - Vu-Quoc, Loc
AU - Humer, Alexander
TI - Deep Learning Applied to Computational Mechanics: A Comprehensive Review, State of the Art, and the Classics
T2 - Computer Modeling in Engineering \& Sciences
PY - 2023
VL - 137
IS - 2
SN - 1526-1506
AB - 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.
KW - Deep learning
KW - breakthroughs
KW - network architectures
KW - backpropagation
KW - stochastic optimization methods from classic to modern
KW - recurrent neural networks
KW - long short-term memory
KW - gated recurrent unit
KW - attention
KW - transformer
KW - kernel machines
KW - Gaussian processes
KW - libraries
KW - Physics-Informed Neural Networks
KW - state-of-the-art
KW - history
KW - limitations
KW - challenges; Applications to computational mechanics; Finite-element matrix integration
KW - improved Gauss quadrature; Multiscale geomechanics
KW - fluid-filled porous media; Fluid mechanics
KW - turbulence
KW - proper orthogonal decomposition; Nonlinear-manifold model-order reduction
KW - autoencoder
KW - hyper-reduction using gappy data; control of large deformable beam
DO - 10.32604/cmes.2023.028130