3 papers
math.NA2026
Trajectory-Based RBF Collocation Method via Closest-Point Embedding for Surface Advection-Diffusion Equations
Xiaobin Li, Leevan Ling, Yizhong Sun
We introduce a Trajectory-Based RBF Collocation (TBRBF) method for solving surface advection-diffusion equations on smooth, compact manifolds. TBRBF decouples advection and diffusi…
math.NA2026
PINN-Based Kolmogorov-Arnold Networks with RAR-D Adaptive Sampling for Solving Elliptic Interface Problems
Zijuan Xin, Chenyao Wang, Feng Shi +1
Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate s…
math.NA2026
Local Regularity Estimation through Sobolev-Scale Norm Profile
Xiaobin Li, Leevan Ling, Yizhong Sun
We develop a kernel-based approach for estimating the spatially varying Sobolev regularity~ of an unknown -variate function~ from scattered sampling data, which quantifies…