Electron neural closure for turbulent magnetosheath simulations: Energy channels

In this work, we introduce a non-local five-moment electron pressure tensor closure parametrized by a fully convolutional neural network (FCNN). Electron pressure plays an important role in generalized Ohm's law, competing with electron inertia. This model is used in the development of a surrogate model for a fully kinetic energy-conserving semi-implicit particle-in-cell simulation of decaying magnetosheath turbulence. We achieve this by training FCNN on a representative set of simulations with a smaller number of particles per cell and showing that our results generalize to a simulation with a large number of particles per cell. We evaluate the statistical properties of the learned equation of state, with a focus on pressure-strain interaction, which is crucial for understanding energy channels in turbulent plasmas. The resulting equation of state learned via FCNN significantly outperforms local closures, such as those learned by multi-layer perceptron (MLP) or double adiabatic expressions. We report that the overall spatial distribution of pressure-strain and its conditional averages are reconstructed well. However, some small-scale features are missed, especially for the off-diagonal components of the pressure tensor. Nevertheless, the results are substantially improved with more training data, indicating favorable scaling and potential for improvement, which will be addressed in future work.