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arXiv · 2501.07809

Conformal mapping based Physics-informed neural networks for designing neutral inclusions

Daehee Cho·Hyeonmin Yun·Jaeyong Lee·Mikyoung Lim
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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.

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Daehee Cho, Hyeonmin Yun, Jaeyong Lee, Mikyoung Lim. 2025-01-14. Conformal mapping based Physics-informed neural networks for designing neutral inclusions. https://arxiv.org/abs/2501.07809

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