Variational training of neural network approximations of solution maps for physical models
type: Item
instance of: scholarly article
title: Variational training of neural network approximations of solution maps for physical models
zbMATH Open document ID: 1435.68292
author: Yingzhou Li
author: Anqi Mao
author: Jianfeng Lu
published in: Journal of Computational Physics
publication date: 2020-07-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/1905.02789
Mathematics Subject Classification ID: 68T07
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 7216813
zbMATH Keywords: neural network
zbMATH Keywords: solution map for PDEs
zbMATH Keywords: fast algorithm
zbMATH Keywords: hierarchical matrix
zbMATH Keywords: unsupervised training
describes a project that uses: Adam
describes a project that uses: DGM
describes a project that uses: PDE-Net
describes a project that uses: TensorFlow
MaRDI profile type: Publication
OpenAlex ID: W2944808962
arXiv ID: 1905.02789
cites work: Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
cites work: Universal approximation bounds for superpositions of a sigmoidal function
cites work: A Multigrid Tutorial, Second Edition
cites work: Solving the quantum many-body problem with artificial neural networks
cites work: An \(O(N)\) direct solver for integral equations on the plane
cites work: The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
cites work: A multiscale neural network based on hierarchical nested bases
cites work: BCR-net: A neural network based on the nonstandard wavelet form
cites work: The black-box fast multipole method
cites work: A fast algorithm for particle simulations
cites work: A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
cites work: Hierarchical Matrices: Algorithms and Analysis
cites work: Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
cites work: Solving high-dimensional partial differential equations using deep learning
cites work: Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations
cites work: Hierarchical interpolative factorization for elliptic operators: integral equations
cites work: Solving for high-dimensional committor functions using artificial neural networks
cites work: Distributed-memory hierarchical interpolative factorization
cites work: Fast construction of hierarchical matrix representation from matrix-vector multiplication
cites work: DGM: a deep learning algorithm for solving partial differential equations
cites work: Superfast Multifrontal Method for Large Structured Linear Systems of Equations
cites work: A kernel-independent adaptive fast multipole algorithm in two and three dimensions
cites work: Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
DOI: 10.1016/J.JCP.2020.109338
description: scientific article