Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

Mikhail Genkin, Owen Hughes, Tatiana A. Engel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system’s dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain.

Original languageEnglish (US)
Article number5986
JournalNature communications
Volume12
Issue number1
DOIs
StatePublished - Dec 1 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology

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