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The paper argues that forecast error alone can't show whether a deep-learning Earth-system model has learned physically sound input-output dependencies. It proposes comparing gradient-based sensitivities against an adjoint reference, or against established physical knowledge where no adjoint exists, as a complementary test. For ML practitioners, the key point is that models with similar accuracy can encode very different sensitivities, so accuracy-only benchmarks can miss physically implausible behavior.
Sensitivity Fidelity Reveals Physical Dependencies Beyond Forecast Accuracy in Deep-Learning Earth-System Models
arXiv:2610.15540v1 Announce Type: new Abstract: Deep-learning models increasingly rival numerical simulation in Earth-system forecasting, yet forecast error alone cannot determine whether their learned input-output dependencies are physically consistent. Here we introduce sensitivity fidelity as an additional criterion: alongside prediction error, model responses to input perturbations should be examined against a trusted reference or established physical knowledge. In an idealized Rayleigh-B\'enard convection benchmark, four surrogate architectures achieved low forecast errors yet encoded markedly different sensitivities. Quantitative comparison with a matched adjoint distinguished the models far more sharply than forecast accuracy and showed that predictive skill and sensitivity fidelity need not coincide, while finite-perturbation experiments further linked these differences to the propagation of initial-condition uncertainty. We then applied this strategy to El Ni\~no-Southern Oscillation prediction, where no adjoint reference exists and learned sensitivities showed event-wise robustness, validity under finite perturbations, and consistency with established precursors. These results identify gradient-based evaluation as a discriminating complement to forecast-error metrics, providing a practical test of whether data-driven Earth-system models learn physically credible dependencies.
Abstract:Deep-learning models increasingly rival numerical simulation in Earth-system forecasting, yet forecast error alone cannot determine whether their learned input-output dependencies are physically consistent. Here we introduce sensitivity fidelity as an additional criterion: alongside prediction error, model responses to input perturbations should be examined against a trusted reference or established physical knowledge. In an idealized Rayleigh-Bénard convection benchmark, four surrogate architectures achieved low forecast errors yet encoded markedly different sensitivities. Quantitative comparison with a matched adjoint distinguished the models far more sharply than forecast accuracy and showed that predictive skill and sensitivity fidelity need not coincide, while finite-perturbation experiments further linked these differences to the propagation of initial-condition uncertainty. We then applied this strategy to El Niño-Southern Oscillation prediction, where no adjoint reference exists and learned sensitivities showed event-wise robustness, validity under finite perturbations, and consistency with established precursors. These results identify gradient-based evaluation as a discriminating complement to forecast-error metrics, providing a practical test of whether data-driven Earth-system models learn physically credible dependencies.
Machine Learning (cs.LG); Atmospheric and Oceanic Physics (physics.ao-ph); Geophysics (physics.geo-ph)
arXiv:2610.15540 [cs.LG]
(or arXiv:2610.15540v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.15540 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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