用共形映射改进神经网络，设计任意形状的隐身包层
Conformal mapping based Physics-informed neural networks for designing neutral inclusions
- 结合共形映射与物理信息神经网络，建模界面函数
- 实现任意形状包层的隐身效果，提升求解稳定性
- 适合研究逆问题和几何建模的学者参考
针对存在非完美边界条件的隐身包层问题，本文聚焦于任意形状包层界面函数的设计。传统物理信息神经网络（PINNs）在此类反问题上表现不佳，为此提出共形映射坐标物理信息神经网络（CoCo-PINNs），将几何函数理论与PINNs结合。CoCo-PINNs通过神经网络训练建模界面函数，有效解决正向与反向问题，实现中性包层效应。该方法显著提升了PINNs在可信度、一致性和稳定性方面的表现。
原文摘要 · Abstract (English)
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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