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arXiv · 2604.20061

Predictivity and Utility of Neural Surrogates of Multiscale PDEs

Karthik Duraisamy
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Abstract

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.

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BibTeXRIS

Karthik Duraisamy. 2026-04-21. Predictivity and Utility of Neural Surrogates of Multiscale PDEs. https://arxiv.org/abs/2604.20061

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