Variational training of neural network approximations of solution maps for physical models
From MaRDI portal
Publication:778301
DOI10.1016/j.jcp.2020.109338zbMath1435.68292arXiv1905.02789OpenAlexW2944808962MaRDI QIDQ778301
Anqi Mao, Yingzhou Li, Jian-feng Lu
Publication date: 2 July 2020
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.02789
Artificial neural networks and deep learning (68T07) NLS equations (nonlinear Schrödinger equations) (35Q55)
Related Items
Using neural networks to accelerate the solution of the Boltzmann equation, A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for deep BSDE solver, A variational framework for computing Wannier functions using dictionary learning, AMS-Net: Adaptive Multiscale Sparse Neural Network with Interpretable Basis Expansion for Multiphase Flow Problems, Control variate method for deep BSDE solver using weak approximation, Accuracy and architecture studies of residual neural network method for ordinary differential equations, Predicting continuum breakdown with deep neural networks, A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks, Solving inverse problems with deep learning, Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning, The Random Feature Model for Input-Output Maps between Banach Spaces, Strong Solutions for PDE-Based Tomography by Unsupervised Learning
Uses Software
Cites Work
- Fast construction of hierarchical matrix representation from matrix-vector multiplication
- A kernel-independent adaptive fast multipole algorithm in two and three dimensions
- The black-box fast multipole method
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
- DGM: a deep learning algorithm for solving partial differential equations
- BCR-net: A neural network based on the nonstandard wavelet form
- Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
- Solving for high-dimensional committor functions using artificial neural networks
- A multiscale neural network based on hierarchical nested bases
- Distributed-memory hierarchical interpolative factorization
- An \(O(N)\) direct solver for integral equations on the plane
- Hierarchical Interpolative Factorization for Elliptic Operators: Integral Equations
- Hierarchical Matrices: Algorithms and Analysis
- Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations
- Superfast Multifrontal Method for Large Structured Linear Systems of Equations
- Universal approximation bounds for superpositions of a sigmoidal function
- A Multigrid Tutorial, Second Edition
- Solving the quantum many-body problem with artificial neural networks
- Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
- Solving high-dimensional partial differential equations using deep learning
- A fast algorithm for particle simulations
