Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data

TL;DR

This paper demonstrates that maximum likelihood estimation can effectively recover the quadratic potential energy parameter in high-dimensional interacting particle systems from single-trajectory data, achieving optimal convergence rates.

Contribution

It shows that vanilla maximum likelihood estimation can accurately estimate interaction potential parameters in high-dimensional systems without regularization.

Findings

MLE achieves optimal convergence rates in mean-field and long-time limits.

Estimation avoids curse-of-dimensionality due to symmetry in particle interactions.

Method applicable to high-dimensional, single-trajectory data.

Abstract

This paper concerns the parameter estimation problem for the quadratic potential energy in interacting particle systems from continuous-time and single-trajectory data. Even though such dynamical systems are high-dimensional, we show that the vanilla maximum likelihood estimator (without regularization) is able to estimate the interaction potential parameter with optimal rate of convergence simultaneously in mean-field limit and in long-time dynamics. This to some extend avoids the curse-of-dimensionality for estimating large dynamical systems under symmetry of the particle interaction.