Equation Discovery for Subgrid-Scale Closures

Editors’ Highlights are summaries of recent papers by AGU’s journal editors.

Source: Journal of Advances in Modeling EarthSystems

Equation discovery methods, a type of machine learning through which equations are learned from dictionaries of plausible equation terms, offer a promising avenue for learning interpretable and often easy-to-implement closures for subgrid-scale fluctuations. Subgrid-scale closure models are crucial in weather and climate simulations, as well as other computational fluid dynamics problems, where small-scale processes cannot be fully resolved due to computational constraints.

Jakhar et al. [2024] demonstrate that common equation discovery algorithms tend to rediscover well-known closure models, such as the nonlinear gradient model (NGM) or other models derivable by Taylor expansions. While the NGM fits data of subgrid-scale fluctuations well, it leads to unstable simulations because it fails to accurately represent the transfer of energy across scales. This highlights a key challenge in current equation discovery methods: the need to incorporate physical knowledge into the learning process.

The authors suggest that including energy transfer constraints in loss functions can improve the accuracy and stability of the discovered models by forcing the inclusion of higher-order terms in closure equations even though they do not strongly affect mean-square errors in representing fluctuations. This research underscores the importance of combining data-driven approaches with physical insights to develop effective closure models for complex systems.

Citation: Jakhar, K., Guan, Y., Mojgani, R., Chattopadhyay, A., & Hassanzadeh, P. (2024). Learning closed-form equations for subgrid-scale closures from high-fidelity data: Promises and challenges. Journal of Advances in Modeling Earth Systems, 16, e2023MS003874. https://doi.org/10.1029/2023MS003874

—Tapio Schneider, Editor, JAMES

Text © 2024. The authors. CC BY-NC-ND 3.0
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