BIMSA > BIMSA Computational Math Seminar BIMSA Computational Math Seminar Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks for Large-Domain PDEs
Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks for Large-Domain PDEs
Organizers
Tahereh Eftekhari , Pipi Hu , Xin Liang , Zhiting Ma , Hamid Mofidi , Chunmei Su , Axel G.R. Turnquist , Li Wang , Fansheng Xiong , Shuo Yang , Wuyue Yang
Speaker
Farinaz Mostajeran
Time
Wednesday, June 24, 2026 2:00 PM - 3:00 PM
Venue
A3-4-312
Online
Zoom 518 868 7656 (BIMSA)
Abstract
Modeling transport processes in environmental and engineering systems often requires solving partial differential equations over large spatial domains. Although Kolmogorov-Arnold Networks have shown strong approximation capabilities and promising performance in scientific computing, their effectiveness can significantly decrease when the input variables are not represented within an appropriate domain. In particular, when the spatial domain becomes wide, these networks may face difficulties in convergence, stability, and accuracy. This talk introduces Scaled-cPIKAN, a physics-informed framework that combines Chebyshev-based Kolmogorov-Arnold Networks with a simple but effective spatial transformation. By appropriately scaling the input coordinates and the governing equation, the proposed method stabilizes training and helps prevent common numerical issues that arise in large-domain PDE problems. Using Neural Tangent Kernel analysis, we provide theoretical insight into why this scaling is essential for achieving fast and consistent convergence. Numerical experiments on several benchmark problems will be discussed to demonstrate the accuracy, efficiency, and robustness of the method. Finally, we will highlight remaining challenges in this area and discuss possible directions for future research.
Speaker Intro
Dr. Farinaz Mostajeran is a Postdoctoral Researcher at the University of Utah's Energy & Intelligence Lab (EiLAB). Her current research focuses on developing neural network-based methods for scientific computing, with a particular emphasis on Kolmogorov-Arnold Networks (KANs), physics-informed learning, and large-scale problems governed by partial differential equations (PDEs). Before joining the University of Utah, she was a Postdoctoral Researcher in the Department of Applied Mathematics at Tarbiat Modares University, where she worked on solving fractional PDEs using hybrid Physics-Informed Neural Networks (PINNs). She received her Ph.D. in Applied Mathematics from Tarbiat Modares University, where her research focused on neural solvers, including physics-informed approaches based on PINNs, radial basis function neural networks, and wavelet neural networks.