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math.NA2026
A Filtered MgNet Solver For Radiative Transfer Equations
Qinchen Song, Xinliang Liu, Lei Zhang
Conventional numerical solvers for the radiative transfer equation (RTE) exhibit severe sensitivity to medium parameters. To address this, we propose an operator learning framework…
math.NA2026
Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
Juncai He, Xinliang Liu, Zitong Tian
This paper studies the numerical approximation of divergence-free vector fields by linearized shallow neural networks, also referred to as random feature models or finite neuron sp…
math.NA2026
Born-Preconditioned Learning for Iterative Neural PDE Solvers
Juntao Wang, Jiwei Jia, Xinliang Liu
Simulating high-frequency waves in spatially varying media remains challenging for both classical iterative methods and neural PDE solvers. We propose Neural Preconditioned Born Se…