# Discovering stochastic dynamical equations from biological time series data

arXiv: https://arxiv.org/abs/2205.02645 · HTML: https://mlsanity.com/paper/2205.02645/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 75 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 3 of 3)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Fundamental limits to learning closed-form mathematical models from data](https://mlsanity.com/paper/2204.02704/) (2022)

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

- [Principled model selection for stochastic dynamics](https://mlsanity.com/paper/2501.10339/) (2025)

## Abstract (arXiv)

Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the role of stochasticity in real datasets. Therefore, the inverse problem of inferring the governing stochastic equations from datasets is important. Here, we present an equation discovery methodology that takes time series data of state variables as input and outputs a stochastic differential equation. We achieve this by combining traditional approaches from stochastic calculus with the equation-discovery techniques. We demonstrate the generality of the method via several applications. First, we deliberately choose various stochastic models with fundamentally different governing equations; yet they produce nearly identical steady-state distributions. We show that we can recover the correct underlying equations, and thus infer the structure of their stability, accurately from the analysis of time series data alone. We demonstrate our method on two real-world datasets -- fish schooling and single-cell migration -- which have vastly different spatiotemporal scales and dynamics. We illustrate various limitations and potential pitfalls of the method and how to overcome them via diagnostic measures. Finally, we provide our open-source codes via a package named PyDaDDy (Python library for Data Driven Dynamics).