Machine-learning-based closures for the 10-moment fluid model

Many plasma phenomena involve physical processes spanning a wide range of spatial and temporal scales. Accurately capturing such multi-scale dynamics with fully kinetic simulations quickly becomes computationally prohibitive. Fluid models therefore remain an essential tool, but their applicability depends critically on the order at which the hierarchy of moment equations derived from the Vlasov equation is truncated and on the assumptions used to approximate neglected higher-order moments. Extended fluid models such as the 10-moment system therefore require appropriate closures to account for kinetic effects encoded in higher-order moments, such as the heat flux.

In this work, we develop data-driven closures for the 10-moment fluid model based on machine learning (ML). Using supervised learning, the ML models learn to predict the six independent components of the divergence of the heat flux tensor from lower-order moments and the electromagnetic fields. The models are trained on data obtained from two-dimensional fully kinetic Vlasov simulations of magnetic reconnection in a Harris current sheet with varying guide field strength, performed with the muphy 2 code (Allmann-Rahn et al., 2023).

We compare different machine learning architectures, including classical multilayer perceptrons (MLPs), fully convolutional networks, and Fourier Neural Operators (FNOs), assessing their ability to capture spatially structured kinetic effects across different physical regimes. The models are evaluated in terms of accuracy, generalization across guide field conditions, and their suitability for incorporation into fluid simulations. Our results highlight the potential of operator-learning approaches for constructing robust, data-driven closures and provide insight into the strengths and limitations of different ML strategies for plasma fluid modeling.