Stress-Testing Reveals Robustness Gaps in Fourier Neural Operators Across Diverse PDEs

Global: Stress-Testing Reveals Robustness Gaps in Fourier Neural Operators Across Diverse PDEs

A recent study introduces a systematic stress‑testing framework for Fourier Neural Operators (FNOs) and evaluates their robustness under distribution shifts, long‑horizon rollouts, and structural perturbations across five qualitatively distinct families of partial differential equations (PDEs).

Framework Overview

The authors shift the focus from optimizing in‑distribution accuracy to deliberately probing failure modes. Their approach incorporates controlled stress tests such as parameter variations, modifications to boundary or terminal conditions, resolution extrapolation examined through spectral analysis, and iterative rollout procedures.

Testing Methodology

To generate a comprehensive assessment, the researchers trained and evaluated 1,000 FNO models spanning dispersive, elliptic, multi‑scale fluid, financial, and chaotic PDE categories. Each model was subjected to the defined stress scenarios to quantify performance degradation.

Key Findings

Results indicate that distribution shifts in parameters or boundary conditions can inflate prediction errors by more than an order of magnitude. In contrast, changes in spatial resolution primarily concentrate error in high‑frequency spectral modes.

Input Perturbation Insights

While generic input perturbations generally did not amplify errors, worst‑case instances—such as localized Poisson perturbations—remained difficult for the models to handle.

Identified Failure Modes

The analysis highlights several recurring vulnerabilities, including spectral bias, compounding integration errors during rollouts, and overfitting to narrowly defined boundary regimes.

Implications for Operator Learning

The authors present a comparative failure‑mode atlas that offers actionable guidance for enhancing the robustness of operator learning techniques.

Future Research Directions

They suggest that targeted architectural adjustments, regularization strategies, and broader training distributions could mitigate the observed shortcomings, pointing to avenues for subsequent investigation.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.