Deep learning in computational mechanics: a review

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Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Physics-informed multi-LSTM networks for metamodeling of nonlinear structures
A tutorial on the adjoint method for inverse problems
Unsupervised discovery of interpretable hyperelastic constitutive laws
Physics-informed neural network for modelling the thermochemical curing process of composite-tool systems during manufacture
A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures
TONR: an exploration for a novel way combining neural network with topology optimization
Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
Predicting the mechanical properties of biopolymer gels using neural networks trained on discrete fiber network data
Accurate and real-time structural topology prediction driven by deep learning under moving morphable component-based framework
Neural networks for topology optimization
Stochastic seismic waveform inversion using generative adversarial networks as a geological prior
A deep energy method for finite deformation hyperelasticity
A surface-to-surface contact search method enhanced by deep learning
FEA-Net: a physics-guided data-driven model for efficient mechanical response prediction
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Prediction of aerodynamic flow fields using convolutional neural networks
On isotropic integrity bases
A geometric multiscale finite element method for the dynamic analysis of heterogeneous solids
Artificial neural network based hole image interpretation techniques for integrated topology and shape optimization
High dimensional integration of smooth functions over cubes
Neural algorithm for solving differential equations
Constrained neural network training and its application to hyperelastic material modeling
Robust topology optimization with low rank approximation using artificial neural networks
ReF-nets: physics-informed neural network for Reynolds equation of gas bearing
A finite element based deep learning solver for parametric PDEs
A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
Finite element approximation of wave problems with correcting terms based on training artificial neural networks with fine solutions
Integrated finite element neural network (I-FENN) for non-local continuum damage mechanics
Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
A new family of constitutive artificial neural networks towards automated model discovery
A deep Fourier residual method for solving PDEs using neural networks
Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
Manifold learning for coherent design interpolation based on geometrical and topological descriptors
Automated discovery of generalized standard material models with EUCLID
Thermodynamics-informed neural networks for physically realistic mixed reality
Deep energy method in topology optimization applications
Determinantal Point Processes for Machine Learning
Computational homogenization of nonlinear elastic materials using neural networks
Dynamic mode decomposition of numerical and experimental data
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Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
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Neural network‐based parameter estimation for non‐linear finite element analyses
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Updating of finite element models using vibration tests
Parallel training of neural networks for finite element mesh decomposition
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Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Subgrid modelling for two-dimensional turbulence using neural networks
Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control
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Data-driven discovery of coordinates and governing equations
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Learning representations by back-propagating errors
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Turbulence Modeling in the Age of Data
Linearly Recurrent Autoencoder Networks for Learning Dynamics
Equilibrium points in n -person games
Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations
A deep convolutional neural network for topology optimization with perceptible generalization ability