Predictivity and Utility of Neural Surrogates of Multiscale PDEs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911613960847360 |
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| author | Duraisamy, Karthik |
| author_facet | Duraisamy, Karthik |
| contents | Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent successes can be explained by facts that also define their limits. Many successful benchmarks live on low-dimensional solution manifolds where any competent reduced model will interpolate well. More fundamentally, neural surrogates systematically under-resolve high-frequency content due to spectral bias, and coarse-graining compounds this problem through irreversible information loss. In many multi-scale problems, no architecture or training procedure can fully recover what the coarse representation discards. Two simple examples are used to characterize spectral bias, coarse-graining and error accumulation. We discuss why medium-range weather prediction on reanalysis data sits in a favorable sweet spot and why this will not generalize to genuinely chaotic multi-scale scenarios. We identify domains where neural surrogates offer genuine value, propose further research on neural-classical hybrids, and call for better reporting standards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Predictivity and Utility of Neural Surrogates of Multiscale PDEs Duraisamy, Karthik Mathematical Physics Chaotic Dynamics 35 I.2.6 Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent successes can be explained by facts that also define their limits. Many successful benchmarks live on low-dimensional solution manifolds where any competent reduced model will interpolate well. More fundamentally, neural surrogates systematically under-resolve high-frequency content due to spectral bias, and coarse-graining compounds this problem through irreversible information loss. In many multi-scale problems, no architecture or training procedure can fully recover what the coarse representation discards. Two simple examples are used to characterize spectral bias, coarse-graining and error accumulation. We discuss why medium-range weather prediction on reanalysis data sits in a favorable sweet spot and why this will not generalize to genuinely chaotic multi-scale scenarios. We identify domains where neural surrogates offer genuine value, propose further research on neural-classical hybrids, and call for better reporting standards. |
| title | Predictivity and Utility of Neural Surrogates of Multiscale PDEs |
| topic | Mathematical Physics Chaotic Dynamics 35 I.2.6 |
| url | https://arxiv.org/abs/2604.20061 |