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

Computer Modeling in Engineering & Sciences 2023年第11期137卷 1069-1343页

作者： Loc Vu-Quoc Alexander Humer Aerospace Engineering University of Illinois at Urbana-ChampaignIL 61801USA Institute of Technical Mechanics Johannes Kepler UniversityA-4040 Linz

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix *** recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in *** hybrid and pure machine learning(ML)methods are *** 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(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural *** 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 *** LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively *** machines,including gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite *** 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 *** and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known *** 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

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