CEENs: causality-enforced evolutional networks for solving time-dependent partial differential equations

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Cites Work

PPINN: parareal physics-informed neural network for time-dependent PDEs
PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs
A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations
A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
Learning time-dependent PDEs with a linear and nonlinear separate convolutional neural network
When and why PINNs fail to train: a neural tangent kernel perspective
Normalizing field flows: solving forward and inverse stochastic differential equations using physics-informed flow models
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
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Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Numerical Methods for Fluid Dynamics
Neural‐network‐based approximations for solving partial differential equations
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Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
A cusp-capturing PINN for elliptic interface problems
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Physics-informed variational inference for uncertainty quantification of stochastic differential equations

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