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

arXiv 2501.07809 ↗First posted 14 Jan 2025cs.LG cs.AI math.APcited by 0

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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.

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References · 13

  1. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  2. 2017GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networkscited by 834
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  4. 2024Challenges in Training PINNs: A Loss Landscape Perspectivecited by 113
  5. 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 87
  6. 2022Physics-informed neural networks for inverse problems in supersonic flowscited by 76
  7. 2023Separable Physics-Informed Neural Networkscited by 66
  8. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 46
  9. 2024PINNACLE: PINN Adaptive ColLocation and Experimental points selectioncited by 32
  10. 2024RoPINN: Region Optimized Physics-Informed Neural Networkscited by 26
  11. 2023Lie Point Symmetry and Physics Informed Networkscited by 24
  12. 2022Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equationscited by 20
1 more
  1. 2022Bi-level Physics-Informed Neural Networks for PDE Constrained Optimization using Broyden's Hypergradientscited by 17

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