Sparse identification of interaction potential from molecular dynamics simulations of dust suspended in a plasma

Identifying the interaction potential between constituents of complex systems is a challenging and important task in colloids, liquid crystals, granular matter, dusty plasma, and many other fields. The explosion of applications in machine learning in recent years has led to many approaches to identify or "discover" this interaction directly from data, often using a neural network approach. An alternative approach—which is both more interpretable and less computationally expensive—is to use sparse regression to deduce an analytic form of the potential from a library of candidate terms. Here, we present the use of the open-source Sparse Identification of Nonlinear Dynamics (SINDy) method in the weak formulation to identify the Yukawa potential from noisy simulated trajectories of point particles interacting through a Yukawa force. We apply this analysis to a molecular dynamics simulation of dust particles suspended in a plasma to learn the modified Yukawa interaction, and discuss possibilities for quantifying anisotropies and non-reciprocity in these systems.