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Conformal mapping based Physics-informed neural networks for designing neutral inclusions
Daehee Cho, Hyeonmin Yun, Jaeyong Lee, Mikyoung Lim · 2025-01-14 · via cs.LG updates on arXiv.org

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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