Building general Langevin models from discrete data sets

TL;DR

This paper introduces a Bayesian inference method to accurately reconstruct second order Langevin models from discrete data, overcoming limitations of naive derivative estimation, and demonstrates its effectiveness on collective motion data.

Contribution

A novel Bayesian approach using higher order discretization schemes for reliable parameter inference of second order Langevin models from finite trajectories.

Findings

Effective parameter estimation with moderately long trajectories.

Method works well even with interacting systems.

Naive methods fail regardless of data resolution.

Abstract

Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in the quantitative reconstruction of the model from experimental data, even in the simple case of equilibrium Langevin dynamics of Hamiltonian systems. We develop a novel Bayesian inference approach to learn the parameters of such stochastic effective models from discrete finite length trajectories. We first discuss the failure of naive inference approaches based on the estimation of derivatives through finite differences, regardless of the time resolution and the length of the sampled trajectories. We then derive, adopting higher order discretization schemes, maximum likelihood estimators for the model parameters that provide excellent results even with moderately long trajectories. We apply our method to second order models of collective motion and show that our results also hold in the presence of interactions.