Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families
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arXiv
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| Format: | Preprint |
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2026
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| author | Shikhman, Lennon |
| author_facet | Shikhman, Lennon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families Shikhman, Lennon Machine Learning 68T07 I.2.6; G.1.8 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. |
| title | Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families |
| topic | Machine Learning 68T07 I.2.6; G.1.8 |
| url | https://arxiv.org/abs/2601.11428 |