20 citations · 34 across the 3 of their papers we have counts for
3 papers
math.NA2020★ 10 cited
Enforcing exact boundary and initial conditions in the deep mixed residual method
Liyao Lyu, Keke Wu, Rui Du +1
In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in cl…
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…