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PyDaddy: A Python package for discovering stochastic dynamical equations from timeseries data

5 May 2022
Arshed Nabeel
Ashwin Karichannavar
Shuaib Palathingal
Jitesh Jhawar
David B. Brückner
M. DannyRaj
Vishwesha Guttal
    AI4TS
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Abstract

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 a software package, PyDaDDy (Python Library for Data Driven Dynamics) that takes time series data as an input and outputs an interpretable SDE. 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).

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