SelectNet: self-paced learning for high-dimensional partial differential equations

DOI10.1016/j.jcp.2021.110444OpenAlexW3000403725WikidataQ115350072 ScholiaQ115350072MaRDI QIDQ2131038

Yiqi Gu, Chao Zhou, Haizhao Yang

Publication date: 25 April 2022

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

Full work available at URL: https://arxiv.org/abs/2001.04860

zbMATH Keywords

convergenceleast square methodhigh-dimensional PDEsself-paced learningdeep neural networksselected sampling

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Related Items (11)

Stationary Density Estimation of Itô Diffusions Using Deep Learning ⋮ Neural networks enforcing physical symmetries in nonlinear dynamical lattices: the case example of the Ablowitz-Ladik model ⋮ Simultaneous neural network approximation for smooth functions ⋮ A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrödinger eigenvalue problems ⋮ A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks ⋮ Artificial neural network solver for time-dependent Fokker-Planck equations ⋮ Gradient and uncertainty enhanced sequential sampling for global fit ⋮ DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations ⋮ Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning ⋮ Active learning based sampling for high-dimensional nonlinear partial differential equations ⋮ Deep Ritz method for elliptical multiple eigenvalue problems

Uses Software

• AdaGrad
• Adam
• DGM
• MentorNet
• D3M

Cites Work

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