Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics  

作　　者：Loc Vu-Quoc Alexander Humer 

机构地区：[1]Aerospace Engineering,University of Illinois at Urbana-Champaign,IL 61801,USA [2]Institute of Technical Mechanics,Johannes Kepler University,A-4040 Linz

出　　处：《Computer Modeling in Engineering & Sciences》2023年第11期1069-1343,共275页工程与科学中的计算机建模（英文）

摘　　要：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.

关 键 词：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 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]