Colloquium / Seminars

Topic：Neural-Accelerated Boundary Integral Solvers: From IBIM to Multi-Level Training
Speaker：Prof. Bing-Ze Lu
　　　　(Department of Mathematics, National Chung Cheng University)
Date time：Dec. 9, 2025 14:00 - 15:00
Venue：SA213
Abstract：
Abstract. Boundary integral equations (BIEs) efficiently reduce elliptic and wave problems to the boundary, but standard implementations require explicit surface parametrizations and produce fully dense matrices. The Implicit Boundary Integral Method (IBIM) avoids parametrization by using a level-set representation and evaluating layer potentials in a tubular neighborhood of a Cartesian grid, at the cost of dense extended operators and high computational expense.

I will present a complementary approach based on spectral-bias-aided multilevel training of neural-network surrogates for IBIM operators. Exploiting the tendency of neural networks to learn low frequencies first, we design a coarse-to-fine training strategy aligned with the IBIM grid hierarchy. This allows information from coarse levels to accelerate training and inference on finer grids, yielding speedups of about 40–600×. I will show results for Laplace and Poisson problems, and briefly discuss extensions to Helmholtz equations and “numerically consistent” machine learning for scientific computing.
Download：Talk_1141209.pdf

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