Physically Consistent Machine Learning-Based Moment Closure for Low-Temperature Plasma Simulations*

Understanding the transport mechanisms in low-temperature plasmas (LTPs) is critical yet challenging due to their complex multiscale phenomena. Traditionally, large-scale plasma simulations utilize fluid approximations, simplifying particle-based physics into moment-based equations. Such procedure requires truncation of the moment hierarchy, where higher-order moments are expressed as functions of lower-order ones. A critical challenge is deciding where to truncate, as improper truncation can significantly impact simulation accuracy [1]. Herein, we propose a learning-based, physically consistent moment closure model for kinetic LTPs. We leverage deep learning to derive optimal truncation level by learning the closure relations for higher-order moments from particle-in-cell (PIC) simulations. Our framework preserves fundamental physics properties, including conservation laws and Lorentz invariance, maintaining structural integrity of the system’s partial differential equations. We demonstrate our approach to analyze two-dimensional PIC simulations of a magnetized plasma column exhibiting significant distortions in density profiles and the development of complex, smaller wavelength structures under strong magnetic fields [2]. By providing a precise method for determining where to truncate the moment hierarchy and maintaining the physics consistency of the learned higher-order closure terms, our model preserves simulation fidelity to kinetic-model standards.

 

[1] Krommes, J. A. (2002). Physics Reports, 360(1-4), 1-352.

[2] Lucken, R. et. al. (2019). Physics of Plasmas, 26(7).