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

arXiv: https://arxiv.org/abs/2501.07809 · HTML: https://mlsanity.com/paper/2501.07809/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 14 Jan 2025.

## Builds on (most cited first, 13 of 13)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Physics-informed neural networks for inverse problems in supersonic flows](https://mlsanity.com/paper/2202.11821/) (2022)
- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios](https://mlsanity.com/paper/2205.07731/) (2022)
- [PINNACLE: PINN Adaptive ColLocation and Experimental points selection](https://mlsanity.com/paper/2404.07662/) (2024)
- [RoPINN: Region Optimized Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.14369/) (2024)
- [Lie Point Symmetry and Physics Informed Networks](https://mlsanity.com/paper/2311.04293/) (2023)
- [Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations](https://mlsanity.com/paper/2203.08501/) (2022)
- [Bi-level Physics-Informed Neural Networks for PDE Constrained Optimization using Broyden's Hypergradients](https://mlsanity.com/paper/2209.07075/) (2022)

## Abstract (arXiv)

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.