A probabilistic framework for learning non‐intrusive corrections to long‐time climate simulations from short‐time training data

Despite advances in high performance computing, accurate numerical simulations of global atmospheric dynamics remain a challenge. The resolution required to fully resolve the vast range scales as well as the strong coupling with—often not fully-understood—physics renders such simulations computationally infeasible over time horizons relevant for long-term climate risk assessment. While data-driven parameterizations have shown some promise of alleviating these obstacles, the scarcity of high-quality training data and their lack of long-term stability typically hinders their ability to capture the risk of rare extreme events. In this work we present a general strategy for training variational (probabilistic) neural network models to non-intrusively correct under-resolved long-time simulations of turbulent climate systems. The approach is based on the paradigm introduced by Barthel Sorensen et al. (2024, https://doi.org/10.1029/2023ms004122) which involves training a post-processing correction operator on under-resolved simulations nudged toward a high-fidelity reference. Our variational framework enables us to learn the dynamics of the underlying system from very little training data and thus drastically improve the extrapolation capabilities of the previous deterministic state-of-the art—even when the statistics of that training data are far from converged. We investigate and compare three recently introduced variational network architectures and illustrate the benefits of our approach on an anisotropic quasi-geostrophic flow. For this prototype model our approach is able to not only accurately capture global statistics, but also the anistropic regional variation and the statistics of multiple extreme event metrics—demonstrating significant improvement over previously introduced deterministic architectures.