A Physics--ML Multi-Fidelity Strategy for Earth System Model Parameter Optimization: A QG Proof-of-Concept

Abstract

Earth System Models rely on tunable subgrid-scale parameterizations, but optimizing these parameters is computationally expensive, particularly when nonlinear interactions require many simulations. We present a hybrid Physics-ML multi-fidelity framework that combines Green's Function Optimization (GFO) with Gaussian Process or Neural Network surrogate optimization. Using a quasi-geostrophic turbulence model, GFO first ranks parameter sensitivities in normalized coordinates and selects a reduced active subset. Nonlinear surrogates then explore this subset using inexpensive 30-day simulations before refining promising candidates with 180-day simulations. Across seven strategies and a 35-member ensemble, GFO-MultiGP and GFO-MultiNN achieved mean improvements of 64.6 percent and 65.2 percent, respectively, while reaching practical saturation after 3,060 and 2,520 simulation-days. The corresponding standalone GP and NN achieved 61.1 percent and 42.0 percent improvements and required 7,740 and 6,660 simulation-days. These results demonstrate an end-to-end sample-efficiency advantage for the tested hybrid pipelines. Because screening, dimensionality reduction, initialization, and fidelity scheduling change simultaneously, their individual contributions are not isolated.