# Electron neural closure for turbulent magnetosheath simulations: energy channels

arXiv: https://arxiv.org/abs/2510.00282 · HTML: https://mlsanity.com/paper/2510.00282/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 95 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [A posteriori learning for quasi-geostrophic turbulence parametrization](https://mlsanity.com/paper/2204.03911/) (2022)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flow](https://mlsanity.com/paper/2206.03198/) (2022)
- [Identification of high order closure terms from fully kinetic simulations using machine learning](https://mlsanity.com/paper/2110.09916/) (2021)
- [Hyperbolic Machine Learning Moment Closures for the BGK Equations](https://mlsanity.com/paper/2401.04783/) (2024)

## Built on by (most cited first, 2 of 2)

- [The Machine Learning Approach to Moment Closure Relations for Plasma: A Review](https://mlsanity.com/paper/2511.22486/) (2025)
- [Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulations](https://mlsanity.com/paper/2601.12614/) (2026)

## Abstract (arXiv)

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.