Reconstructing fluid closures using supervised Machine Learning

The process of deriving fluid equations from the Vlasov equation for collisionless plasmas involves a fundamental challenge known as the closure problem. This problem consists of the fact that the temporal evolution of any particle moment—such as density, current, pressure, or heat flux—includes terms that depend on the next higher-order moment. Consequently, truncating the description at the nth order necessitates approximating the contributions of the (n+1)th order moment within the evolution equation for the nth moment. The choice of truncation level and the assumptions underlying these approximations play a critical role in determining the accuracy with which the resulting fluid model captures kinetic processes.

The work presented here focuses on reconstructing higher-order moments using only lower-order moments, along with the electric and magnetic fields, as inputs. We apply supervised machine learning to train models that predict higher-order moments, specifically the divergence of the heat flux tensor, in simulations of magnetic reconnection within a Harris current sheet under varying background guide fields. All simulations we use are obtained with the muphy 2 code (Allmann-Rahn et al. 2023). Fully kinetic Vlasov simulations, which provide complete physical information, serve as the ground truth. The reconstructed moments are incorporated into fluid simulations, and their impact on the simulation dynamics is analyzed. We evaluate the models' ability to generalize across different guide field conditions and compare the performance of the machine learning-based closures with commonly used closures in fluid simulations.