Maximum likelihood estimation of potential energy in interacting particle systems from 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.

References in corpus (4)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• A Mean Field View of the Landscape of Two-Layers Neural Networks
• Nonparametric inference of interaction laws in systems of agents from trajectory data
• Learning interaction kernels in heterogeneous systems of agents from multiple trajectories

Cited by in corpus (4)

• Neural parameter calibration for large-scale multi-agent models
• Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories
• Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation
• On the coercivity condition in the learning of interacting particle systems