This repo contains a jupyter notebook that illustrates the inference of a fundamental plasma physics equation -- the kinetic Vlasov equation -- from the data of a first-principles particle-in-cell (PIC) simulation using sparse regression techniques. The data for this example can be obtained here.
The example presented here corresponds to the first example discussed in Data-driven discovery of reduced plasma physics models from fully kinetic simulations by Alves and Fiuza (2022). This work included other examples involving the inference of the fundamental hierarchy of plasma equations -- from the kinetic Vlasov equation to magnetohydrodynamics -- from the data of fully kinetic PIC simulations. This work suggested that sparse regression techniques can offer a promising route to accelerate the development of new reduced theoretical models of complex nonlinear plasma phenomena and to design computationally efficient algorithms for multiscale plasma simulations.
The sparse regression techniques used here are inspired by the recent works of Brunton et al. (2016), Rudy et al. (2017) and Schaeffer (2017). In order to robustly handle the discrete particle noise that characterizes the data of fully kinetic PIC simulations, the underlying differential equations are inferred in their integral form, rather than their differential form. This technqiue was used in Alves and Fiuza (2022); closely related integral formulation techniques to robustly deal with noisy data have also been discussed in Schaeffer and McCalla (2017), Reinbold et al. (2020) and Messenger and Bortz (2021).