Title: Data-driven discovery of dynamical models in biology Show Chinese title

Title: 数据驱动的生物学动力学模型发现

Abstract: Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales. Classical modeling derives explicit governing equations, often systems of differential equations, by combining mechanistic assumptions, experimental observations, and known physical laws. The growing complexity of biological processes has, however, motivated complementary data-driven methods that aim to infer model structure directly from measurements, often without specifying equations a priori. In this review, we survey approaches for model discovery in biological dynamical systems, focusing on three methodological families: regression-based methods, network-based architectures, and decomposition techniques. We compare their ability to address three core goals: forecasting future states, identifying interactions, and characterizing system states. Representative methods are applied to a common benchmark, the Oregonator model, a minimal nonlinear oscillator that captures shared design principles of chemical and biological systems. By highlighting strengths, limitations, and interpretability, we aim to guide researchers in selecting tools for analyzing complex, nonlinear, and high-dimensional dynamics in the life sciences. Show Chinese abstract

Abstract: 动力系统理论描述了相互作用的量如何随时间和空间变化，从分子振荡器到大尺度生物模式。 这样的系统通常涉及非线性反馈、延迟和跨尺度的相互作用。 经典建模通过结合机制假设、实验观察和已知的物理定律来推导显式的控制方程，通常是微分方程组。 然而，生物过程的日益复杂性已经促使了补充的数据驱动方法，这些方法旨在直接从测量中推断模型结构，通常不需要事先指定方程。 在本综述中，我们调查了生物动力系统中的模型发现方法，重点集中在三种方法学家族上：基于回归的方法、基于网络的架构和分解技术。 我们比较了它们在解决三个核心目标方面的能力：预测未来状态、识别相互作用以及表征系统状态。 代表性方法被应用于一个共同的基准——Oregonator模型，这是一个最小的非线性振荡器，能够捕捉化学和生物系统的共同设计原则。 通过突出其优势、局限性和可解释性，我们旨在指导研究人员选择工具来分析生命科学中的复杂、非线性和高维动力学。