One of the biggest challenges in climate science and weather forecasting is predicting the effects of turbulence at spatial scales smaller than the resolution of atmospheric and oceanic models. Simplified sets of equations known as closure models can predict the statistics of this “subgrid” turbulence, but existing closure models are prone to dynamic instabilities or fail to account for rare, high-energy events. Now Karan Jakhar at the University of Chicago and his colleagues have applied an artificial-intelligence (AI) tool to data generated by numerical simulations to uncover an improved closure model [1]. The finding, which the researchers subsequently verified with a mathematical derivation, offers insights into the multiscale dynamics of atmospheric and oceanic turbulence. It also illustrates that AI-generated prediction models need not be “black boxes,” but can be transparent and understandable.

The team trained their AI—a so-called equation-discovery tool—on “ground-truth” data that they generated by performing computationally costly, high-resolution numerical simulations of several 2D turbulent flows. The AI selected the smallest number of mathematical functions (from a library of 930 possibilities) that, in combination, could reproduce the statistical properties of the dataset. Previously, researchers have used this approach to reproduce only the spatial structure of small-scale turbulent flows. The tool used by Jakhar and collaborators filtered for functions that correctly represented not only the structure but also energy transfer between spatial scales.

They tested the performance of the resulting closure model by applying it to a computationally practical, low-resolution version of the dataset. The model accurately captured the detailed flow structures and energy transfers that appeared in the high-resolution ground-truth data. It also predicted statistically rare conditions corresponding to extreme-weather events, which have challenged previous models.