An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

TL;DR

This paper introduces an unsupervised machine-learning checkpoint-restart algorithm for particle-in-cell simulations that preserves physical invariants and reduces input/output costs, improving simulation fidelity and efficiency.

Contribution

It presents a novel Gaussian mixture-based CR algorithm that guarantees conservation laws and Gauss' law, enhancing PIC simulation restart capabilities.

Findings

High-fidelity restart with conservation of charge, momentum, and energy.

Potential for significant input/output savings.

Improved PIC solution fidelity at given particle resolution.

Abstract

We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm features a particle compression stage and a particle reconstruction stage, where a continuum particle distribution function (PDF) is constructed and resampled, respectively. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. We demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.