演講者：呂秉澤教授 (國立中正大學數學系)

日   期：2026 年 06 月 17 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：Spectral-Bias-Aided Multilevel Neural Networks for Implicit Boundary Integral Equations

摘   要：

In this talk, we present a neural-network-based framework for solving implicit boundary integral equations (IBIEs). The unknown surface potential is represented by a neural network and determined through a least-squares optimization problem derived from the integral equation.
The central idea is to exploit the spectral bias of neural networks to design a multilevel training strategy. Since neural networks naturally learn low-frequency components before high-frequency ones, we first train on coarse discretizations to efficiently capture smooth solution features and then progressively refine the approximation on finer levels. This approach significantly reduces training cost while maintaining accuracy. We further analyze the method through the Neural Tangent Kernel (NTK) framework to explain the observed acceleration.
Numerical experiments demonstrate substantial computational gains. Compared with conventional single-level training, the proposed multilevel strategy achieves a 4–5× speedup. For exterior Helmholtz scattering problems, it attains accuracy comparable to conventional solvers while reducing computation time from over 12,000 seconds to approximately 200 seconds.