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Long-term stability is a critical property for deep learning-baseddata-driven digital twins of the Earth system. Such data-driven digital twinsenable sub-seasonal and seasonal predictions of extreme environmental events,probabilistic forecasts, that require a large number of ensemble members, andcomputationally tractable high-resolution Earth system models where expensivecomponents of the models can be replaced with cheaper data-driven surrogates.Owing to computational cost, physics-based digital twins, though long-termstable, are intractable for real-time decision-making. Data-driven digitaltwins offer a cheaper alternative to them and can provide real-timepredictions. However, such digital twins can only provide short-term forecastsaccurately since they become unstable when time-integrated beyond 20 days.Currently, the cause of the instabilities is unknown, and the methods that areused to improve their stability horizons are ad-hoc and lack rigorous theory.In this paper, we reveal that the universal causal mechanism for theseinstabilities in any turbulent flow is due to \textit{spectral bias} wherein,\textit{any} deep learning architecture is biased to learn only the large-scaledynamics and ignores the small scales completely. We further elucidate howturbulence physics and the absence of convergence in deep learning-basedtime-integrators amplify this bias leading to unstable error propagation.Finally, using the quasigeostrophic flow and ECMWF Reanalysis data as testcases, we bridge the gap between deep learning theory and fundamental numericalanalysis to propose one mitigative solution to such instabilities. We developlong-term stable data-driven digital twins for the climate system anddemonstrate accurate short-term forecasts, and hundreds of years of long-termstable time-integration with accurate mean and variability.

Long-term instabilities of deep learning-based digital twins of the climate system: The cause and a solution