# Identification of high order closure terms from fully kinetic simulations using machine learning

arXiv: https://arxiv.org/abs/2110.09916 · HTML: https://mlsanity.com/paper/2110.09916/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 31 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Built on by (most cited first, 5 of 5)

- [Data-driven modeling of Landau damping by physics-informed neural networks](https://mlsanity.com/paper/2211.01021/) (2022)
- [Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems](https://mlsanity.com/paper/2505.18857/) (2025)
- [Electron neural closure for turbulent magnetosheath simulations: energy channels](https://mlsanity.com/paper/2510.00282/) (2025)
- [The Machine Learning Approach to Moment Closure Relations for Plasma: A Review](https://mlsanity.com/paper/2511.22486/) (2025)
- [A Competitive Learning Approach for Specialized Models: A Solution for Complex Physical Systems with Distinct Functional Regimes](https://mlsanity.com/paper/2307.10496/) (2023)

## Abstract (arXiv)

Simulations of large-scale plasma systems are typically based on a fluid approximation approach. These models construct a moment-based system of equations that approximate the particle-based physics as a fluid, but as a result lack the small-scale physical processes available to fully kinetic models. Traditionally, empirical closure relations are used to close the moment-based system of equations, which typically approximate the pressure tensor or heat flux. The more accurate the closure relation, the stronger the simulation approaches kinetic-based results. In this paper, new closure terms are constructed using machine learning techniques. Two different machine learning models, a multi-layer perceptron and a gradient boosting regressor, synthesize a local closure relation for the pressure tensor and heat flux vector from fully kinetic simulations of a 2D magnetic reconnection problem. The models are compared to an existing closure relation for the pressure tensor, and the applicability of the models is discussed. The initial results show that the models can capture the diagonal components of the pressure tensor accurately, and show promising results for the heat flux, opening the way for new experiments in multi-scale modeling. We find that the sampling of the points used to train both models play a capital role in their accuracy.