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This paper concerns the parameter estimation problem for the quadraticpotential energy in interacting particle systems from continuous-time andsingle-trajectory data. Even though such dynamical systems arehigh-dimensional, we show that the vanilla maximum likelihood estimator(without regularization) is able to estimate the interaction potentialparameter with optimal rate of convergence simultaneously in mean-field limitand in long-time dynamics. This to some extend avoids thecurse-of-dimensionality for estimating large dynamical systems under symmetryof the particle interaction.

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