How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning

Magnetic geometry has a significant effect on plasma turbulence. We model and analyze this dependence using machine learning methods and a dataset of >200,000 nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence in diverse geometries. At fixed gradients, the turbulent heat flux varies between geometries by several orders of magnitude. Interpretable regression and classification techniques are applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features along the field, akin to translation invariance in computer vision. Multiple regression models including convolutional neural networks (CNNs) and decision trees achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection, and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important feature relates to geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow extension to more features for higher accuracy. The dataset, openly available online, can also be used to test other proposed surrogates; many published proxies do correlate well with the data.