Abstract:Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on a fixed benchmark distribution but generalization under structured shifts in coefficients, boundary conditions, discretization, and rollout horizon. Yet evaluation is still often dominated by in-distribution test error, making robustness difficult to assess. We introduce a standardized stress-testing framework for neural PDE solvers under deployment-relevant shift. We instantiate it on three representative architectures -- Fourier Neural Operators (FNOs), a DeepONet-style model, and convolutional neural operators (CNOs) -- across five qualitatively different PDE families: dispersive, elliptic, multi-scale fluid, financial, and chaotic systems. Across 750 trained models, we measure robustness using baseline-normalized degradation factors together with spectral and rollout diagnostics. The resulting comparisons reveal that strong in-distribution accuracy does not reliably predict robustness, and that failure patterns depend jointly on architecture and PDE family. Our results provide a clearer basis for evaluating robustness claims in neural PDE solvers and suggest that function-space generalization under structured shift should be treated as a first-class evaluation target.
| Comments: | 13 pages, 7 figures, 5 tables. Submitted for peer review |
| Subjects: | Machine Learning (cs.LG) |
| MSC classes: | 68T07 |
| ACM classes: | I.2.6; G.1.8 |
| Cite as: | arXiv:2601.11428 [cs.LG] |
| (or arXiv:2601.11428v5 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2601.11428 arXiv-issued DOI via DataCite |
From: Lennon Shikhman [view email]
[v1]
Fri, 16 Jan 2026 16:47:44 UTC (819 KB)
[v2]
Sat, 24 Jan 2026 18:44:50 UTC (819 KB)
[v3]
Tue, 27 Jan 2026 15:32:48 UTC (819 KB)
[v4]
Mon, 13 Apr 2026 15:27:39 UTC (58 KB)
[v5]
Tue, 21 Apr 2026 01:29:51 UTC (60 KB)
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