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math.NA2026
Boundary-preserving randomized neural network methods for Poisson equations on general two- and three-dimensional domains
Huifang Zhou
In this paper, we propose a boundary-preserving randomized neural network method for Poisson equations with Dirichlet boundary conditions in two and three dimensions. A linear lift…
math.NA2024
Improved randomized neural network methods with boundary processing for solving elliptic equations
Huifang Zhou, Zhiqiang Sheng
We present two improved randomized neural network methods, namely RNN-Scaling and RNN-Boundary-Processing (RNN-BP) methods, for solving elliptic equations such as the Poisson equat…
math.NA2024
A finite volume method preserving the invariant region property for the quasimonotone reaction-diffusion systems
Huifang Zhou
We present a finite volume method preserving the invariant region property (IRP) for the reaction-diffusion systems with quasimonotone functions, including nondecreasing, decreasin…