Inferring the dynamics of underdamped stochastic systems

Abstract

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference (ULI), which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.

References in corpus (15)

• Novel type of phase transition in a system of self-driven particles
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Scale-free correlations in bird flocks
• 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
• Moving and staying together without a leader
• Collective behaviour without collective order in wild swarms of midges
• Noise-Induced Schooling of Fish
• Learning force fields from stochastic trajectories
• High-Performance Reconstruction of Microscopic Force Fields from Brownian Trajectories
• Contact enhancement of locomotion in spreading cell colonies
• Emergent Bistability and Switching in a Nonequilibrium Crystal
• Disentangling the Behavioural Variability of Confined Cell Migration
• Langevin equations from experimental data: the case of rotational diffusion in granular media

Cited by in corpus (33)

• Physics-constrained, low-dimensional models for MHD: First-principles and data-driven approaches
• Learning the dynamics of cell-cell interactions in confined cell migration
• Autonomous inference of complex network dynamics from incomplete and noisy data
• Nonlinear stochastic modeling with Langevin regression
• Learning Mean-Field Equations from Particle Data Using WSINDy
• Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories
• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
• 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
• Sparse inference and active learning of stochastic differential equations from data
• Thermodynamic Uncertainty Relation in Interacting Many-Body Systems
• Extracting Forces from Noisy Dynamics in Dusty Plasmas
• Discovering dynamic laws from observations: the case of self-propelled, interacting colloids
• Bézier interpolation improves the inference of dynamical models from data
• Information-driven transitions in projections of underdamped dynamics
• Learning minimal representations of stochastic processes with variational autoencoders
• Data-driven model construction for anisotropic dynamics of active matter
• Large deviations of the stochastic area for linear diffusions
• Statistical Inference of 1D Persistent Nonlinear Time Series and Application to Predictions
• Learning Dynamics from Multicellular Graphs with Deep Neural Networks
• From predicting to learning dissipation from pair correlations of active liquids
• Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks
• Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
• Force-free kinetic inference of entropy production
• From reductionism to realism: Holistic mathematical modelling for complex biological systems
• Inferring nonlinear fractional diffusion processes from single trajectories
• Elastic interactions compete with persistent cell motility to drive durotaxis
• Dynamics of azimuthal thermoacoustic modes in imperfectly symmetric annular geometries
• Thermodynamic inference of correlations in nonequilibrium collective dynamics
• Coarse-graining nonequilibrium diffusions with Markov chains
• Learning general pair interactions between self-propelled particles
• A Likelihood Approach for Inference of Population Heterogeneity in Particle Ensembles with Second-Order Langevin Dynamics