Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data
Xiaohui Chen
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.
Topics & Concepts
Curse of dimensionalityEstimatorMathematicsTrajectoryParticle systemQuadratic equationApplied mathematicsRegularization (linguistics)Limit (mathematics)Rate of convergenceDynamical systems theoryEstimation theoryStatistical physicsInteracting particle systemMathematical optimizationStatisticsMathematical analysisComputer sciencePhysicsOperating systemAstronomyGeometryComputer networkChannel (broadcasting)Continuous-time stochastic processStochastic differential equationQuantum mechanicsArtificial intelligenceModel Reduction and Neural NetworksProtein Structure and DynamicsMarkov Chains and Monte Carlo Methods