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math.NA2026
A modified projected walk on spheres method for elliptic equations on high-dimensional embedded manifolds: algorithm and error estimates
Zhiyuan Hui, Changtao Sheng, Bihao Su +1
In this paper, we propose a modified projected Walk on Spheres method (MPWoS) for screened Poisson equations on embedded manifolds. The method employs local extensions together wit…
math.NA2026
PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations
Jizu Huang, Yue Qian, Tao Zhou
Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent ye…
math.NA2026
Decoupled Divergence-Free Neural Networks Basis Method for Incompressible Fluid Problems
Jinbao Cheng, Jianguo Huang, Haoqin Wang +1
We propose a decoupled divergence-free neural networks basis (Decoupled-DFNN) method for solving incompressible flow problems, including the Stokes and Navier-Stokes equations. To…