MIM: a deep mixed residual method for solving high-order partial differential equations

DOI10.1016/j.jcp.2021.110930OpenAlexW4226402869WikidataQ114163376 ScholiaQ114163376MaRDI QIDQ2133607

Minxin Chen, Jingrun Chen, Liyao Lyu, Zhen Zhang

Publication date: 4 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.04146

zbMATH Keywords

deep learningdeep Galerkin methoddeep mixed residual methodhigh-order partial differential equations

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (14)

Solving multiscale elliptic problems by sparse radial basis function neural networks ⋮ Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations ⋮ Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees ⋮ A deep first-order system least squares method for solving elliptic PDEs ⋮ Capturing the diffusive behavior of the multiscale linear transport equations by asymptotic-preserving convolutional deeponets ⋮ DNN-HDG: a deep learning hybridized discontinuous Galerkin method for solving some elliptic problems ⋮ Asymptotic-preserving neural networks for multiscale time-dependent linear transport equations ⋮ Adaptive Learning Rate Residual Network Based on Physics-Informed for Solving Partial Differential Equations ⋮ A priori error estimate of deep mixed residual method for elliptic PDEs ⋮ An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations ⋮ A deep branching solver for fully nonlinear partial differential equations ⋮ Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions ⋮ BI-GreenNet: learning Green's functions by boundary integral network ⋮ A deep domain decomposition method based on Fourier features

Uses Software

• L-BFGS
• PyTorch
• Adam
• DGM
• D3M

Cites Work

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