aiqbench analysis
This paper provides a theoretical analysis using the Neural Tangent Kernel to explain why adversarial training effectively mitigates spectral bias and stiffness in Physics-Informed Neural Networks (PINNs). By leveraging GAN discriminators, the authors derive a practical algorithm that significantly improves accuracy on high-frequency solutions compared to standard methods.
When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective
arXiv:2605.15959v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial training based on generative adversarial networks (GANs) has recently gained surprisingly strong empirical results in improving training, but the underlying mechanisms remain elusive. To this end, we propose a new analysis framework for adversarially trained PINNs, based on the key observation of how the discriminator in GANs can influence the training dynamics of PINNs. The framework first provides a much needed theoretical grounding to why and when adversarial training is effective in PINNs, then presents a unified analysis of GANs variants in such training, and finally leads to a new, practical, efficient training algorithm for PINNs. Empirical results demonstrate that our method can significantly reduce the pathology of PINNs training, thereby providing better models with superior performances, often several magnitudes more accurate than alternative methods.
Abstract:Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial training based on generative adversarial networks (GANs) has recently gained surprisingly strong empirical results in improving training, but the underlying mechanisms remain elusive. To this end, we propose a new analysis framework for adversarially trained PINNs, based on the key observation of how the discriminator in GANs can influence the training dynamics of PINNs. The framework first provides a much needed theoretical grounding to why and when adversarial training is effective in PINNs, then presents a unified analysis of GANs variants in such training, and finally leads to a new, practical, efficient training algorithm for PINNs. Empirical results demonstrate that our method can significantly reduce the pathology of PINNs training, thereby providing better models with superior performances, often several magnitudes more accurate than alternative methods.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2605.15959 [cs.LG]
(or arXiv:2605.15959v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.15959 Focus to learn more arXiv-issued DOI via DataCite
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