PINN achieves 91% accuracy in 3D noisy heat diffusion vs 36% for FDM and 3.3x better error reduction in physical experiment, with efficiency gains in high dimensions.
Xu,Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations, posted on 2024, DOI 10.48550/arXiv.2407.10836
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A survey organizing AI methods for inverse PDE problems into inverse problems, inverse design, and control categories, covering applications and future challenges like physics-informed models and uncertainty quantification.
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Overcoming the Limits of Finite Difference Method; Physics-Informed Neural Network for Noisy High-Dimensional Heat Diffusion
PINN achieves 91% accuracy in 3D noisy heat diffusion vs 36% for FDM and 3.3x better error reduction in physical experiment, with efficiency gains in high dimensions.
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Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects
A survey organizing AI methods for inverse PDE problems into inverse problems, inverse design, and control categories, covering applications and future challenges like physics-informed models and uncertainty quantification.