A mesh-free method using piecewise deep neural network for elliptic interface problems

DOI10.1016/j.cam.2022.114358zbMath1491.65158arXiv2005.04847OpenAlexW3022977644MaRDI QIDQ2141617

Cuiyu He, Lin Mu, Xiaozhe Hu

Publication date: 25 May 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.04847

zbMATH Keywords

neural networksadaptive methodinterface problemsmesh-freeleast-square methodDNN

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Boundary value problems for second-order elliptic equations (35J25) Neural networks for/in biological studies, artificial life and related topics (92B20) Second-order parabolic equations (35K10) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (14)

A discontinuity capturing shallow neural network for elliptic interface problems ⋮ Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient ⋮ Physics-Informed Neural Networks for Solving Dynamic Two-Phase Interface Problems ⋮ A deep first-order system least squares method for solving elliptic PDEs ⋮ A meshless method based on the generalized finite difference method for three-dimensional elliptic interface problems ⋮ A cusp-capturing PINN for elliptic interface problems ⋮ An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications ⋮ HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network ⋮ A Discontinuity and Cusp Capturing PINN for Stokes Interface Problems with Discontinuous Viscosity and Singular Forces ⋮ DNN-HDG: a deep learning hybridized discontinuous Galerkin method for solving some elliptic problems ⋮ High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems ⋮ A deep learning method for multi-material diffusion problems based on physics-informed neural networks ⋮ Multi-scale fusion network: a new deep learning structure for elliptic interface problems ⋮ Numerical approximation based on immersed finite element method for elliptic interface optimal control problem

Uses Software

• CutFEM
• TensorFlow
• Adam
• gvnn
• DGM

Cites Work

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