Poster at APS 2021
I presented a poster at the 2021 meeting of the American Physical Society Division of Plasma Physics (APS-DPP 2021). The poster's title was "Sparse Identification of Nonlinear Moment Closure Dynamics" (changed from "A Data-Driven Analysis of Non-Equilibrium Transport in the Magnetized Kelvin-Helmholtz Instability").
The poster PDF may be found here.
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, \( \chi \).