Forcing and Diagnosing Failure Modes of Fourier Neural Operators (arxiv.org)

A recent study has unveiled a systematic framework for evaluating the performance of Fourier Neural Operators (FNOs) across various families of partial differential equations (PDEs). While FNOs have demonstrated considerable aptitude in modeling complex solution maps, concerns linger about their robustness under changing conditions. This research introduces controlled stress tests addressing diverse scenarios such as parameter shifts, boundary condition alterations, and resolution adjustments, revealing critical vulnerabilities in FNOs, including significant error escalation—sometimes exceeding an order of magnitude—when faced with distribution shifts. This work is crucial for the AI/ML community as it highlights the limitations and failure modes of FNOs, serving as a comparative atlas that can guide future enhancements in operator learning. By identifying specific errors related to spectral bias and integration challenges, the findings encourage the development of more resilient models capable of maintaining accuracy across a range of operational contexts. With over 1,000 models evaluated, the insights gained could significantly inform efforts to improve robustness and generalizability in machine learning applications related to PDEs and other complex systems.