  Stochastic differential equations (SDEs) are an important framework to model
dynamics with randomness, as is common in most biological systems. The inverse
problem of integrating these models with empirical data remains a major
challenge. Here, we present an equation discovery methodology that takes time
series data as an input, analyses fine scale fluctuations and outputs an
interpretable SDE that can correctly capture long-time dynamics of data. We
achieve this by combining traditional approaches from stochastic calculus
literature with state-of-the-art equation discovery techniques. We validate our
approach on synthetic datasets, and demonstrate the generality and
applicability of the method on two real-world datasets of vastly different
spatiotemporal scales: (i) collective movement of fish school where
stochasticity plays a crucial role, and (ii) confined migration of a single
cell, primarily following a relaxed oscillation. We make the method available
as an easy-to-use, open-source Python package, PyDaddy (Python Library for Data
Driven Dynamics).
