22 citations · 76 across the 17 of their papers we have counts for
Showing 2020Show all
3 papers · 1 filter
math.OC2020★ 5 cited
A consensus-based global optimization method with adaptive momentum estimation
Jingrun Chen, Shi Jin, Liyao Lyu
Objective functions in large-scale machine-learning and artificial intelligence applications often live in high dimensions with strong non-convexity and massive local minima. First…
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…