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math.NA2024
Multiscale Neural Networks for Approximating Green's Functions
Wenrui Hao, Rui Peng Li, Yuanzhe Xi +2
Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solv…
math.NA2024
On pattern formation in the thermodynamically-consistent variational Gray-Scott model
Wenrui Hao, Chun Liu, Yiwei Wang +1
In this paper, we explore pattern formation in a four-species variational Gary-Scott model, which includes all reverse reactions and introduces a virtual species to describe the bi…
cs.LG2024★ 2 cited
Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations
Wenrui Hao, Xinliang Liu, Yahong Yang
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology,…