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DY: Fachverband Dynamik und Statistische Physik
DY 6: Machine Learning in Dynamics and Statistical Physics I
DY 6.11: Vortrag
Montag, 9. März 2026, 12:15–12:30, HÜL/S186
Learning spatiotemporal patterns from mean-field data — •Edmilson Roque dos Santos1 and Tiago Pereira2 — 1MPI-PKS,Germany — 2University of São Paulo, Brazil
Networks of coupled dynamical systems are fundamental models across the sciences, from physics to neuroscience. Despite their success, the governing equations of such systems are often unknown, limiting our ability to predict and control their dynamics. A major current effort is to learn these governing equations directly from data. However, existing approaches typically require access to the time series of all node states, which is rarely available outside controlled experiments. In most realistic scenarios, only aggregate or mean-field data, such as linear combinations of node states, can be measured. In this case, learning the governing equations from mean-field data inevitably becomes a secondary goal, since one must first learn the network trajectory that generated the observed measurements. This task is inherently challenging because distinct network states can yield identical macroscopic observations. Here, we address the problem of learning the network trajectory from random mean-field measurements. We show that accurate reconstruction becomes possible when the network exhibits structured spatiotemporal patterns, such as traveling waves. By representing these patterns sparsely in the Fourier domain, we leverage compressive sensing theory to formulate a convex optimization problem that robustly reconstructs the network trajectory. We illustrate our findings using a unidirectional ring of coupled Stuart-Landau oscillators.
Keywords: Compressive Sensing; Governing Equations; Spatiotemporal patterns; Mean-field data; Time series analysis