Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families

arXiv:2601.11428v4 Announce Type: replace Abstract: Neural PDE solvers have shown strong performance on standard benchmarks, but their robustness under deployment-relevant distribution shifts remains insufficiently characterized. We present a systematic stress-testing framework for evaluating neural PDE solvers across five qualitatively different PDE families -- dispersive, elliptic, multi-scale fluid, financial, and chaotic systems -- under controlled shifts in parameters, boundary or terminal conditions, resolution, rollout horizon, and input perturbations. The framework is instantiated on three representative architectures: Fourier Neural Operators (FNOs), DeepONet, and convolutional neural operators (CNOs). Across 750 trained models, we evaluate robustness using baseline-normalized degradation factors together with spectral and rollout diagnostics. This setup is designed to distinguish failure patterns that are shared across architectures from those that are architecture- or PDE-specific. Overall, the paper is framed as an evaluation study rather than a new architecture paper, with the goal of providing a clearer basis for assessing robustness claims in neural PDE solvers.