无需真实数据，用物理响应就能高效选最优神经算子。
Shared Physics Responses Recover Hidden Rankings in Neural Operator Libraries
- 用单个锚点线性化方程响应，同时评分所有模型
- 准确恢复超99.6%的模型偏好和99.0%最优检查点
- 适合无真值数据时部署科学代理模型的场景
当缺乏高保真参考解时，部署阶段选择最优神经算子极具挑战。我们证明，在平方希尔伯特空间损失下，有限模型库的排序严格依赖于候选模型差异的低维张成，可通过单个基于锚点的控制方程线性化响应同时评估所有模型。该共享物理诊断在流体、反应-扩散和波动动力学的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，并建立了可计算的充分条件，可严格认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残差大小，该框架实现了无需真实数据的可靠且高效的科学代理部署。
原文摘要 · Abstract (English)
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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