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

TL;DR

This paper introduces CoCo-PINNs, a novel neural network approach that combines conformal mapping with physics-informed neural networks to design neutral inclusions with arbitrary shapes, improving stability and accuracy.

Contribution

The paper develops CoCo-PINNs, integrating geometric function theory with PINNs to effectively solve inverse problems in designing neutral inclusions of arbitrary shapes.

Findings

CoCo-PINNs successfully model interface functions for neutral inclusions.

The approach improves credibility, consistency, and stability of PINNs.

Effective for inverse design problems with complex geometries.

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.