2 papers
cs.LG2025
Understanding Generalization in Physics Informed Models through Affine Variety Dimensions
Takeshi Koshizuka, Issei Sato
Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However…
cs.LG2024
Understanding the Expressivity and Trainability of Fourier Neural Operator: A Mean-Field Perspective
Takeshi Koshizuka, Masahiro Fujisawa, Yusuke Tanaka +1
In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the rando…