共享物理响应在神经算子库中恢复隐藏排名

中文摘要 AI 辅助

在部署时选择最优的神经算子预测，当缺少高保真参考解时颇具挑战性。我们证明，在平方希尔伯特空间损失下，有限模型库的排名严格依赖于候选差异的低维张成，这使得我们可以利用控制方程的单个基于锚点的线性化响应，同时对所有模型打分。这种共享物理诊断在流体、反应-扩散和波动动力学的各类傅里叶与卷积算子库中，准确恢复了超过99.6%的成对偏好和99.0%的最优检查点。此外，修正后的物理代理常优于最佳单个候选模型，且我们建立了可计算的充分条件，能严格验证强单调离散化的精确决策。通过利用局部动力学响应而非原始缺陷幅度，该框架无需真值数据即可实现科学代理的可靠且高效部署。

英文摘要

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.

发表机构

• Changchun University of Science and Technology（长春理工大学）
• School of Physics（物理学院）

机构由 AI 辅助整理，请以论文原文为准。