Hybrid Quadrature-Based Moment Methods for Kinetic Plasma Simulations

Abstract

Quadrature-based moment methods (QBMM) provide a reduced-order alternative to direct kinetic simulations but are affected by a closure approximation error that accumulates over time, limiting their accuracy for long-time simulations. This work develops hybrid QBMM models for kinetic plasma simulations, in which a neural network correction is added to a baseline QBMM variant (QMOM or HyQMOM) to mitigate this error. Two canonical test cases are considered: the collisionless Sod shock tube and linear Landau damping. For the shock tube, a multi-layer perceptron trained on a spatial stencil of moments and regularized by a Hankel realizability penalty significantly reduces the L1 error across the first four moments relative to the uncorrected QMOM baseline. For Landau damping, an LSTM recurrent neural network operating on a truncated Fourier representation of the moment state is trained to predict corrections to the right-hand side of the moment transport equations. This architecture recovers the oscillatory structure of the electric field energy, and reduces the late-time density deviation from equilibrium by factors of approximately 30 (QMOM) and 8.5 (HyQMOM) relative to the uncorrected baselines. For the Landau damping test case, the hybrid scheme for HyQMOM emerges as the more practical model since it requires a simpler correction architecture and is better suited to future nonlinear extensions. These results demonstrate that the accuracy of quadrature-based moment methods for plasma physics can be improved through data-driven corrections, furthering their potential as an efficient tool for plasma modeling.