A data-driven analysis of non-equilibrium transport in the magnetized Kelvin-Helmholtz instability

Collisional kinetic equations such as the Boltzmann equation provide a detailed

description of plasma physics, but their numerical solution can present a

challenge. Particle methods suffer from stochastic noise, and the direct

solution of kinetic equations in 6D phase space is out of reach computationally.

A common class of reduced models are the moment methods, which

integrate the kinetic equation over velocity space to obtain an infinite coupled

hierarchy of unknowns, requiring an ansatz for the distribution function to

close the hierarchy. Near local thermodynamic equilibrium (LTE), the Boltzmann

H-Theorem indicates that the natural choice of ansatz is a Maxwellian. However,

in regimes far from LTE, the available choices of ansatz are less satisfactory.

This work applies a data-driven approach to the analysis of the moment closure

problem. Full particle distribution data from a continuum kinetic simulation of

the magnetized Kelvin-Helmholtz instability are analyzed using the Sparse

Identification of Nonlinear Dynamics (SINDy) method. It is verified that mass,

momentum and energy conservation are witnessed by the SINDy analysis. SINDy is

then applied to derive approximate higher-order transport relations, and the

regimes of applicability of these relations are discussed. Finally, we explore

the departure from LTE, as measured by the dynamics of the 1-norm of deviation

from the local Maxwellian, χ.