  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.
