📝 SummarXiv

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.