Evaluating the Adversarial Robustness for Fourier Neural Operators

TL;DR

This paper investigates the adversarial robustness of Fourier Neural Operators used in scientific discovery, revealing their vulnerability to input perturbations and providing tools for robustness assessment.

Contribution

First study to analyze adversarial robustness of FNOs in scientific applications, offering a sensitivity analysis tool and evaluation principles.

Findings

FNO robustness degrades rapidly with increased perturbations

Non-simplistic cases like Darcy and Navier are more vulnerable

Provides a new framework for robustness evaluation in scientific ML models

Abstract

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.