Identifying dust particle interaction potential in dusty plasma from simulation data using sparse regression

Identification of particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the advent of machine learning (ML) methods, this interaction can be extracted from particle position data, leading to a generalizable expression which is applicable in different systems. Methods such as sparse regression promise to lead to an interpretable model that can generalize well, while avoiding unnecessary complexity due to overfitting. In this work, we present the use of the Sparse Identification of Nonlinear Dynamics (SINDy) [1] with the weak formulation [2] to learn equations of motion for noisy data from simple simulations of two and three dust particles suspended in a plasma. This analysis is extended to data from a hybrid kinetic simulation of dust and ions, the Dynamic Response of Ions And Dust (DRIAD), to learn an experimentally relevant anisotropic interaction potential. The application of these methods to experimental dusty plasma data is discussed, particularly in the case of glass box experiments and microgravity environments such as Plasmakristall-4.