Learning Reduced Nonlinear Plasma Models from Data

This thesis explores the use of Machine Learning (ML) techniques, with a particular emphasis on Sparse Regression (SR), to obtain interpretable reduced nonlinear plasma models from data of first-principle Particle-In-Cell (PIC) simulations.

In order to become familiar with the SR technique, its advantages and limitations, SR is first applied to the data of the electron two-stream instability. Particular emphasis is given to exploring the importance of using an integral formulation of SR to deal with intrinsically noisy data from finite particle statistics.

SR is then applied to the study of nonlinear ion-acoustic dynamics on plasmas. PIC simulations are used to identify the rich dynamics of nonlinear perturbations in plasmas. SR is used to recover the ion momentum equation from data of these simulations under different conditions.

Motivated by the results on ion-acoustic waves, SR technique is then applied to recover the Kortweg de-Vries (KdV) equation, both on data generated directly from the analytical solutions and from fully-kinetic PIC simulations. It is shown that in weak non-linear regimes, as appropriate for the KdV equation, even very low noise levels put strong limitations for recovering high order derivatives. These results have important implications for future applications of SR to discover reduced nonlinear models from data. These implications and future research directions are discussed.