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).

翻译：随机微分方程（SDEs）是描述具有随机性动力学的核心框架，这常见于大多数生物系统中。将此类模型与经验数据相结合的逆问题仍是一项重大挑战。本文提出一款软件包PyDaDDy（数据驱动动力学的Python库），该软件以时间序列数据为输入，输出可解释的随机微分方程。我们通过融合随机微积分文献中的经典方法与前沿方程发现技术来实现这一目标。在合成数据集上验证了方法的有效性，并在两个时空尺度迥异的真实世界数据集上证明了方法的通用性与适用性：（i）随机性起关键作用的鱼群集体运动，（ii）主要遵循松弛振荡的单细胞受限迁移。我们以易于使用的开源Python软件包PyDaddy（数据驱动动力学的Python库）形式提供该方法。