Many real-world systems—from physiology and neuroscience to climate and finance—are inherently non-stationary, operating far from equilibrium with structure that evolves in time. This talk presents a physical and data-driven framework for understanding such systems through time-varying oscillatory dynamics. Central to this approach is the concept of chronotaxic systems: non-autonomous oscillators with dynamically stable, time-dependent characteristic frequencies, providing a principled way to model robustness and adaptability without assuming stationarity or time-asymptotic behaviour.

I will discuss how instantaneous frequency, nonlinear mode decomposition, and multiscale ridge extraction enable the learning of interpretable latent dynamics from complex, noisy time series where classical spectral methods fail. These methods form the basis of the MODA toolbox and support reliable separation, tracking, and interpretation of interacting components with evolving amplitudes and frequencies.

The framework further enables inference of time-varying interactions and causal structure using wavelet-based coherence, information-theoretic measures, and Bayesian dynamical inference, including in networks with non-stationary coupling. Applications will be drawn primarily from physiology and neuroscience—such as neurovascular coupling, anaesthesia-induced phase transitions, and ageing—but the methods generalise across domains, including physical, engineered, and socio-economic systems.

The talk highlights how physically grounded models of non-stationary dynamics complement machine learning by providing interpretable representations, principled constraints, and reliable inference in settings where purely data-driven approaches struggle.