# When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective

arXiv: https://arxiv.org/abs/2605.15959 · HTML: https://mlsanity.com/paper/2605.15959/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 3 of 3)

- [Solving Differential Equations Using Neural Network Solution Bundles](https://mlsanity.com/paper/2006.14372/) (2020)
- [DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networks](https://mlsanity.com/paper/2209.07081/) (2022)
- [Neural Tangent Kernel of Neural Networks with Loss Informed by Differential Operators](https://mlsanity.com/paper/2503.11029/) (2025)

## Built on by (most cited first, 1 of 1)

- [Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave It](https://mlsanity.com/paper/2609.32864/) (2026)

## Abstract (arXiv)

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.