20 citations · 32 across the 5 of their papers we have counts for
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math.NA2021★ 3 cited
A Deep Learning Based Discontinuous Galerkin Method for Hyperbolic Equations with Discontinuous Solutions and Random Uncertainties
Jingrun Chen, Shi Jin, Liyao Lyu
We propose a deep learning based discontinuous Galerkin method (D2GM) to solve hyperbolic equations with discontinuous solutions and random uncertainties. The main computational ch…
math.NA2020★ 20 cited
MIM: A deep mixed residual method for solving high-order partial differential equations
Liyao Lyu, Zhen Zhang, Minxin Chen +1
In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method (DGM) uses the P…
math.NA2019★ 4 cited
Quasi-Monte Carlo sampling for machine-learning partial differential equations
Jingrun Chen, Rui Du, Panchi Li +1
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined…