# Evaluating the Adversarial Robustness for Fourier Neural Operators

arXiv: https://arxiv.org/abs/2204.04259 · HTML: https://mlsanity.com/paper/2204.04259/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 9 references that are in the map.
- First posted on arXiv 8 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Holistic Adversarial Robustness of Deep Learning Models](https://mlsanity.com/paper/2202.07201/) (2022)

## Built on by (most cited first, 2 of 2)

- [Ricci flow regularization in latent spaces for the forward learning of partial differential equations](https://mlsanity.com/paper/2401.14591/) (2024)
- [Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators](https://mlsanity.com/paper/2604.13316/) (2026)

## Abstract (arXiv)

In recent years, Machine-Learning (ML)-driven approaches have been widely used in scientific discovery domains. Among them, the Fourier Neural Operator (FNO) was the first to simulate turbulent flow with zero-shot super-resolution and superior accuracy, which significantly improves the speed when compared to traditional partial differential equation (PDE) solvers. To inspect the trustworthiness, we provide the first study on the adversarial robustness of scientific discovery models by generating adversarial examples for FNO, based on norm-bounded data input perturbations. Evaluated on the mean squared error between the FNO model's output and the PDE solver's output, our results show that the model's robustness degrades rapidly with increasing perturbation levels, particularly in non-simplistic cases like the 2D Darcy and the Navier cases. Our research provides a sensitivity analysis tool and evaluation principles for assessing the adversarial robustness of ML-based scientific discovery models.