A discontinuity capturing shallow neural network for elliptic interface problems

DOI10.1016/j.jcp.2022.111576OpenAlexW4294958351MaRDI QIDQ2675625

Wei-Fan Hu, Ming-Chih Lai, Te-Sheng Lin

Publication date: 24 September 2022

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

Full work available at URL: https://arxiv.org/abs/2106.05587

zbMATH Keywords

deep learningelliptic interface problemhigh-dimensional PDEsdiscontinuity capturingshallow neural network

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Parabolic equations and parabolic systems (35Kxx)

Related Items (7)

JAX-DIPS: neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities ⋮ A cusp-capturing PINN for elliptic interface problems ⋮ An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications ⋮ A shallow physics-informed neural network for solving partial differential equations on static and evolving surfaces ⋮ 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 ⋮ High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems

Uses Software

• Matlab
• L-BFGS-B
• L-BFGS
• LBFGS-B
• DiffSharp
• Adam
• DGM

Cites Work

• Unnamed Item
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• Neural‐network‐based approximations for solving partial differential equations
• Spectral Methods in MATLAB
• Solving high-dimensional partial differential equations using deep learning
• The Immersed Interface Method
• Approximation by superpositions of a sigmoidal function

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