3 papers
math.NA2026
Physics-guided correction for operator learning under model misspecification
Lei Ma, Nicolas Boullé, Yu-Sen Yang +2
Physics-informed operator learning provides an efficient framework for approximating solution operators of partial differential equations by combining observational data with gover…
math.OC2026
Distortion-minimized de-homogenization for optimization of cell-size distribution in TPMS structures
Hiroki Kawabe, Kaito Ohtani, Yusibo Yang +2
This paper presents a homogenized topology optimization (TO) method for spatially optimizing cell-size distribution of triply-periodic minimal surface (TPMS) structures, with high…
physics.comp-ph2025
Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems
Yu-Sen Yang, Ling Guo, Xiaodan Ren
Multi-scale PDE problems present significant challenges in scientific computing. While conventional MLP-based deep learning methods exhibit spectral bias in resolving multi-scale f…