Building general Langevin models from discrete data sets

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.

arXiv commentwe correct previous inaccuracy about a reference; 29 pages, 9 figures

References in corpus (17)

• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Statistical mechanics for natural flocks of birds
• Dimensionality and dynamics in the behavior of C. elegans
• Superfluid transport of information in turning flocks of starlings
• Inverse statistical problems: from the inverse Ising problem to data science
• Flocking and turning: a new model for self-organized collective motion
• Dynamic scaling in natural swarms
• Local equilibrium in bird flocks
• Diffusion of individual birds in starling flocks
• Dynamical maximum entropy approach to flocking
• Learning force fields from stochastic trajectories
• Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise
• Path-space variational inference for non-equilibrium coarse-grained systems
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Dynamical renormalization group approach to the collective behaviour of swarms
• Spatio-temporal correlations in models of collective motion ruled by different dynamical laws
• Renormalization group crossover in the critical dynamics of field theories with mode coupling terms

Cited by in corpus (16)

• Understanding causation via correlations and linear response theory
• Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls
• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media
• Maximally predictive states: from partial observations to long timescales
• Optimal reaction coordinates and kinetic rates from the projected dynamics of transition paths
• Bézier interpolation improves the inference of dynamical models from data
• Information-driven transitions in projections of underdamped dynamics
• Data-driven model construction for anisotropic dynamics of active matter
• Collective response to local perturbations: how to evade threats without losing coherence
• A Renormalization Group Approach to Connect Discrete- and Continuous-Time Descriptions of Gaussian Processes
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
• Force-free kinetic inference of entropy production
• Assessing the Suitability of the Langevin Equation for Analyzing Measured Data Through Downsampling
• Inferring nonlinear fractional diffusion processes from single trajectories
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable