Global climate models (GCMs) are the main tools for understanding and
predicting climate change. However, due to limited numerical resolutions, these
models suffer from major structural uncertainties; e.g., they cannot resolve
critical processes such as small-scale eddies in atmospheric and oceanic
turbulence. Thus, such small-scale processes have to be represented as a
function of the resolved scales via closures (parametrization). The accuracy of
these closures is particularly important for capturing climate extremes.
Traditionally, such closures are based on heuristics and simplifying
assumptions about the unresolved physics. Recently, supervised-learned
closures, trained offline on high-fidelity data, have been shown to outperform
the classical physics-based closures. However, this approach requires a
significant amount of high-fidelity training data and can also lead to
instabilities. Reinforcement learning is emerging as a potent alternative for
developing such closures as it requires only low-order statistics and leads to
stable closures. In Scientific Multi-Agent Reinforcement Learning (SMARL)
computational elements serve a dual role of discretization points and learning
agents. We leverage SMARL and fundamentals of turbulence physics to learn
closures for prototypes of atmospheric and oceanic turbulence. The policy is
trained using only the enstrophy spectrum, which is nearly invariant and can be
estimated from a few high-fidelity samples (these few samples are far from
enough for supervised/offline learning). We show that these closures lead to
stable low-resolution simulations that, at a fraction of the cost, can
reproduce the high-fidelity simulations' statistics, including the tails of the
probability density functions. The results demonstrate the high potential of
SMARL for closure modeling for GCMs, especially in the regime of scarce data
and indirect observations.

通过使用 SMARL 和湍流物理的基本原理，仅使用几个高保真样本进行了训练，并针对大气和海洋湍流的原型学习了闭合模型，结果表明 SMARL 在 GCMs 的闭合建模方面具有高潜力，尤其是在数据稀缺和间接观测的情况下。