New Method Ranks Neural Operators Without Ground Truth.

Selecting the best neural operator model for deployment in scientific applications is a significant challenge, especially when high-fidelity ground-truth solutions are unavailable for comparison. This paper introduces a novel and highly efficient method to overcome this hurdle. It shows that by analyzing the low-dimensional span of differences between candidate models under a squared Hilbert-space loss, one can rank an entire library of models simultaneously. The core of the method involves using a single, anchor-based linearized response of the governing physical equation as a "shared physical diagnostic." This diagnostic doesn't require the true solution but rather probes the local dynamical response of the system. The researchers found that this proxy accurately recovered over 99.6% of pairwise model preferences and 99.0% of optimal checkpoints across various Fourier and convolutional operator libraries. The technique was validated across diverse physical phenomena, including fluid dynamics, reaction-diffusion processes, and wave dynamics. Remarkably, this corrected physical proxy often outperformed even the best individual candidate models. The study also establishes computable conditions that rigorously guarantee exact decisions for strongly monotone discretizations, enabling reliable and highly efficient deployment of scientific surrogates without the need for ground-truth data.