Electron neural closure for turbulent magnetosheath simulations: energy channels

TL;DR

The paper tackles electron-scale energy dynamics in collisionless magnetosheath turbulence by learning a non-local, five-moment electron pressure tensor closure with a Fully Convolutional Neural Network (FCNN). Trained on fully kinetic ECsim data and validated against higher-particle-count simulations, the FCNN closure yields strong fidelity for diagonal pressure components and meaningful, though more challenging, recovery of off-diagonal terms, along with accurate pressure-strain energy channels evaluated through scale-filtering diagnostics. Compared to a local MLP closure and symbolic double-adiabatic closures, FCNN delivers substantially improved representations of pressure, anisotropy, agyrotropy, and PiD, enabling credible energy budgeting in reduced-order models. The results indicate that FCNN-based non-local closures can serve as efficient surrogates for multiscale magnetospheric simulations, with clear paths toward extension to broader parameter spaces, three-dimensional geometry, and ROM integration to enable large-domain studies with faithful electron-scale physics.

Abstract

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 generalise 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.

Figures (9)

• Figure 1: The input/output and architecture of the Fully Convolutional Neural Network (FCNN), top, and Multi Layer Perceptron (MLP), bottom. The images on the left are being fed into both architectures using either a patch-based approach, as indicated by a green frame in the case of FCNN, or a point-based approach, as indicated by a green arrow in the case of MLP. On the right, the output pressure tensor is plotted. The internal architecture of FCNN consists of 3 convolutional layers with (number of channels, kernel dimension 1, kernel dimension 2) indicated on top. The green arrows indicate the application of activation functions and batch normalization. MLP consists of 4 layers, each with 100 neurons.
• Figure 2: Evaluation of the MLP and FCNN closures on a frame $t = 500 \,\omega_{pi}^{-1}$, with run B1 serving as a test set (see Table \ref{['tab:sim_datasplit']}). Rows correspond to different pressure tensor components ($P_{xx}$, and $P_{xy}$), while columns correspond to (a,d) ground truth, (b,e) FCNN predictions, and (c,f) MLP predictions. Each quantity corresponds to the pressure tensor components, with the corresponding color bar on the right. To provide a reference, we add contours of $A_z$, which is equivalent to the flux function in 2D.
• Figure 3: Plot of z-component of heat flux $q_z$ at $t=500 \; \omega_{pi}^{-1}$ for (a) ground truth, (b) FCNN prediction. Heat flux vector plots are equipped with a corresponding color bar on the right. To provide a reference, we add contours of $A_z$, which is equivalent to the flux function in 2D.
• Figure 4: Plot of agyrotropy (equation \ref{['eq:agyrotropy']}) and incompressible pressure-strain $PiD$ at $t = 500 \; \omega_{pi}^{-1}$ for (a) agyrotropy ground truth, (b) FCNN prediction of agyrotropy, (c) MLP prediction of agyrotropy, (d) $PiD$ ground truth, (e) FCNN prediction of $PiD$, (f) MLP prediction of $PiD$. To provide a reference, we add contours of $A_z$, which is equivalent to the flux function in 2D.
• Figure 5: Temperature anisotropy vs. $\beta_\|$ plots (a.k.a. Brazil plot) histograms with counts represented on the rainbow colormap for (a) ground truth. (b) FCNN prediction. (c) MLP prediction. The dashed line corresponds to the onset of whistler instability, while the dot-dashed line corresponds to the onset of the firehose instability.