A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks

DOI10.1016/j.jcp.2022.110939OpenAlexW3160376246WikidataQ114163373 ScholiaQ114163373MaRDI QIDQ2135256

Lexing Ying, Haoya Li

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/2105.03480

zbMATH Keywords

neural networkeigenvalue problempartial differential equationsemigroup method

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Artificial intelligence (68Txx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Related Items (2)

A deep learning method for computing eigenvalues of the fractional Schrödinger operator ⋮ Deep Ritz method for elliptical multiple eigenvalue problems

Uses Software

• ImageNet
• Adam
• BERT
• AlexNet

Cites Work

• Unnamed Item
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Solving high-dimensional eigenvalue problems using deep neural networks: a diffusion Monte Carlo like approach
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Solving for high-dimensional committor functions using artificial neural networks
• Solving the quantum many-body problem with artificial neural networks

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