5 papers
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…
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…
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…
Chebyshev Spectral Neural Networks for Solving Partial Differential Equations
Pengsong Yin, Shuo Ling, Wenjun Ying
The purpose of this study is to utilize the Chebyshev spectral method neural network(CSNN) model to solve differential equations. This approach employs a single-layer neural networ…
A Hybrid Kernel-Free Boundary Integral Method with Operator Learning for Solving Parametric Partial Differential Equations In Complex Domains
Shuo Ling, Liwei Tan, Wenjun Ying
The Kernel-Free Boundary Integral (KFBI) method presents an iterative solution to boundary integral equations arising from elliptic partial differential equations (PDEs). This meth…