Long-term stability and physical consistency are critical properties for AI-based weather models if they are going to be used for subseasonal-to-seasonal forecasts or beyond, e.g., climate change projection. However, current AI-based weather models can only provide short-term forecasts accurately since they become unstable or physically inconsistent when time-integrated beyond a few weeks or a few months. Either they exhibit numerical blow-up or hallucinate unrealistic dynamics of the atmospheric variables, akin to the current class of autoregressive large language models. The cause of the instabilities is unknown, and the methods that are used to improve their stability horizons are ad-hoc and lack rigorous theory. In this paper, we reveal that the universal causal mechanism for these instabilities in any turbulent flow is due to \textit{spectral bias} wherein, \textit{any} deep learning architecture is biased to learn only the large-scale dynamics and ignores the small scales completely. We further elucidate how turbulence physics and the absence of convergence in deep learning-based time-integrators amplify this bias, leading to unstable error propagation. Finally, using the quasi-geostrophic flow and European Center for Medium-Range Weather Forecasting (ECMWF) Reanalysis data as test cases, we bridge the gap between deep learning theory and numerical analysis to propose one mitigative solution to such unphysical behavior. We develop long-term physically-consistent data-driven models for the climate system and demonstrate accurate short-term forecasts, and hundreds of years of time-integration with accurate mean and variability.

翻译：若要将基于AI的天气模型应用于次季节至季节尺度预报乃至气候变化预估等领域，长期稳定性和物理一致性是其必须具备的关键特性。然而，当前的AI天气模型仅能提供准确的短期预报，因为在时间积分超过数周或数月后，它们会变得不稳定或物理不一致。这些模型要么出现数值爆炸，要么产生大气变量不真实的动力学幻象，类似于当前自回归大语言模型存在的问题。不稳定的成因尚不明确，用于改善其稳定时间范围的方法也缺乏严谨理论依据且具有临时性。本文揭示了任何湍流中这类不稳定现象的普遍因果机制源于\textit{谱偏差}，即\textit{任何}深度学习架构都存在仅偏重于学习大尺度动力学而完全忽略小尺度动力学的倾向。我们进一步阐明了湍流物理学与基于深度学习的时间积分器缺乏收敛性如何放大这种偏差，从而导致不稳定的误差传播。最后，我们以准地转流和欧洲中期天气预报中心再分析数据为测试案例，弥合深度学习理论与数值分析之间的鸿沟，为此类非物理行为提出一种缓解方案。我们开发了气候系统的长期物理一致数据驱动模型，并展示了其准确的短期预报能力，以及能够进行数百年时间积分并保持准确的均值和变率特征。