Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries

2026-08-20

AI Summary

该研究解决了在缺乏高精度参考解时选择最优神经算子预测的问题，通过共享物理响应方法准确恢复模型排名。

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.

Problem

• neural operator
• high-fidelity reference
• model selection

Innovation

• shared physical response
• neural operator library
• squared Hilbert-space loss
• anchor-based linearized response
• strongly monotone discretizations