2 citations · 6 across the 7 of their papers we have counts for
4 papers · 1 filter
Energy Approach from -Graph to Continuum Diffusion Model with Connectivity Functional
Yahong Yang, Sun Lee, Jeff Calder +1
We derive an energy-based continuum limit for -graphs endowed with a general connectivity functional. We prove that the discrete energy and its continuum counterpart d…
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…
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…
A randomized Newton's method for solving differential equations based on the neural network discretization
Qipin Chen, Wenrui Hao
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method…