Antonio C. Costa | Paris Brain Institute, Sorbonne University
Comparing Dynamical Systems from Data: A Multiscale Approach
Variability across realizations of dynamical systems is a hallmark of complexity, appearing in ecosystems, neural circuits, and beyond. Yet comparing such systems remains challenging: when dynamics are nonlinear and span multiple timescales, standard metrics based on summary statistics often obscure meaningful differences. Animal behavior offers a compelling case. Persistent differences in how individuals explore and interact with their environment can influence evolutionary fitness and shield populations against environmental change. Similar forms of variability arise, for example, in neurological disorders, where differences in motor symptoms may hold the key to developing more personalized therapies. To address this challenge, we introduce a computational framework for comparing dynamical systems directly from data. We encode nonlinear dynamics probabilistically by inferring transfer operators from time series, then define a distance metric between these operators to capture structure across multiple timescales. Tailored to finite, noisy datasets, the approach identifies principal axes of variation and enables robust clustering of individual trajectories. We demonstrate this framework in various out-of-equilibrium systems, including bacterial chemotaxis and larval zebrafish locomotion, where the inferred axes of behavioral variation reflect underlying physiological variables and developmental histories. More broadly, our approach provides a principled, data-driven way to resolve and interpret variability in complex dynamical systems across domains.