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In recent years, Machine-Learning (ML)-driven approaches have been widelyused in scientific discovery domains. Among them, the Fourier Neural Operator(FNO) was the first to simulate turbulent flow with zero-shot super-resolutionand superior accuracy, which significantly improves the speed when compared totraditional partial differential equation (PDE) solvers. To inspect thetrustworthiness, we provide the first study on the adversarial robustness ofscientific discovery models by generating adversarial examples for FNO, basedon norm-bounded data input perturbations. Evaluated on the mean squared errorbetween the FNO model's output and the PDE solver's output, our results showthat the model's robustness degrades rapidly with increasing perturbationlevels, particularly in non-simplistic cases like the 2D Darcy and the Naviercases. Our research provides a sensitivity analysis tool and evaluationprinciples for assessing the adversarial robustness of ML-based scientificdiscovery models.

Evaluating the Adversarial Robustness for Fourier Neural Operators