Conformal mapping based Physics-informed neural networks for designing neutral inclusions
Machine Learning
2026-02-03 v2 Artificial Intelligence
Analysis of PDEs
Abstract
We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse problem, leading to the development of Conformal Mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrate geometric function theory with PINNs. CoCo-PINNs effectively solve forward-inverse problems by modeling the interface function through neural network training, which yields a neutral inclusion effect. This approach enhances the performance of PINNs in terms of credibility, consistency, and stability.
Cite
@article{arxiv.2501.07809,
title = {Conformal mapping based Physics-informed neural networks for designing neutral inclusions},
author = {Daehee Cho and Hyeonmin Yun and Jaeyong Lee and Mikyoung Lim},
journal= {arXiv preprint arXiv:2501.07809},
year = {2026}
}