# Identifying stochastic governing equations from data of the most probable transition trajectories

arXiv: https://arxiv.org/abs/2002.10251 · HTML: https://mlsanity.com/paper/2002.10251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs](https://mlsanity.com/paper/2307.09142/) (2023)

## Abstract (arXiv)

Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a governing stochastic dynamical system, from its time-series data of the most probable transition trajectory. By the Onsager-Machlup theory, the most probable transition trajectory satisfies the corresponding Euler-Lagrange equation, which is a second order deterministic ordinary differential equation involving the drift term and diffusion coefficient. We first estimate the coefficients of the Euler-Lagrange equation based on the data of the most probable trajectory, and then we calculate the drift and diffusion coefficients of the governing stochastic dynamical system. These two steps involve sparse regression and optimization. Finally, we illustrate our method with an example and some discussions.