3 papers
math.NA2026
Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps
Shuo Ling, Wenjun Ying, Han Zhou
Dirichlet-to-Neumann (DtN) maps send boundary values of a partial differential equation (PDE) solution to its normal derivative on the boundary. Learning such maps across varying d…
math.NA2026
Neural Evolutionary Kernel Method: A Knowledge-Guided Framework for Solving Evolutionary PDEs
Shuo Ling, Wenjun Ying, Zhen Zhang
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerg…
math.NA2026
A Stabilized Numerical Framework for Necrotic Tumor Growth via Coupled Boundary Integral and Obstacle Solvers
Yu Feng, Shuo Ling, Wenjun Ying +1
We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulatin…