3 papers
math.NA2026
A mixed residual method for biharmonic equations in spectral Barron spaces
Mengjia Bai, Kuo Gai, Shuai Lu
We propose a mixed residual method (MIM) for numerically solving the biharmonic equation with nonhomogeneous clamped boundary conditions. By establishing the well-posedness of the…
math.NA2025
Uniformly accurate structure-preserving neural surrogates for radiative transfer
Mengjia Bai, Jingrun Chen, Keke Wu
In this work, we propose a uniformly accurate, structure-preserving neural surrogate for the radiative transfer equation with periodic boundary conditions based on a multiscale par…
math.NA2024
Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations
Mengjia Bai, Jingrun Chen, Rui Du +1
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including…