Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries
arXiv:2608.20441v1 Announce Type: new Abstract: Selecting the optimal neural-operator prediction during deployment is challenging when high-fidelity reference solutions are unavailable. We demonstrate that under a squared Hilbert-space loss, ranking a finite model library depends strictly on the low-dimensional span of candidate differences, allowing us to score all models simultaneously using a single anchor-based linearized response of the governing equation. This shared physical diagnostic accurately recovered over 99.6\% of pairwise preferences and 99.0\% of optimal checkpoints across diverse Fourier and convolutional operator libraries for fluid, reaction-diffusion, and wave dynamics. Furthermore, the corrected physical proxy frequently outperformed the best individual candidates, and we establish computable sufficient conditions that rigorously certify exact decisions for strongly monotone discretizations. By exploiting the local dynamical response rather than raw defect magnitude, this framework enables the reliable and highly efficient deployment of scientific surrogates without requiring ground-truth data.
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[Submitted on 20 Aug 2026]
Title:Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries
View a PDF of the paper titled Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries, by Hanbing Liang and 1 other authors
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Abstract:Selecting the optimal neural-operator prediction during deployment is challenging when high-fidelity reference solutions are unavailable. We demonstrate that under a squared Hilbert-space loss, ranking a finite model library depends strictly on the low-dimensional span of candidate differences, allowing us to score all models simultaneously using a single anchor-based linearized response of the governing equation. This shared physical diagnostic accurately recovered over 99.6\% of pairwise preferences and 99.0\% of optimal checkpoints across diverse Fourier and convolutional operator libraries for fluid, reaction-diffusion, and wave dynamics. Furthermore, the corrected physical proxy frequently outperformed the best individual candidates, and we establish computable sufficient conditions that rigorously certify exact decisions for strongly monotone discretizations. By exploiting the local dynamical response rather than raw defect magnitude, this framework enables the reliable and highly efficient deployment of scientific surrogates without requiring ground-truth data.
Subjects:
Machine Learning (cs.LG); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Cite as: arXiv:2608.20441 [cs.LG]
(or arXiv:2608.20441v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.20441
arXiv-issued DOI via DataCite (pending registration)
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From: Hanbing Liang [view email] [v1] Thu, 20 Aug 2026 14:10:09 UTC (1,093 KB)
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