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DY: Fachverband Dynamik und Statistische Physik
DY 20: Data analytics for dynamical systems I (Focus Session joint with DY and BP) (joint session SOE/BP/CPP/DY)
DY 20.7: Vortrag
Dienstag, 17. März 2020, 11:45–12:00, GÖR 226
Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States — •Jonas Isensee1,2, George Datseris1,2, and Ulrich Parlitz1,2 — 1Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany — 2Institut für Dynamik komplexer Systeme, Georg-August Universität Göttingen, Germany
Understanding dynamics in spatially extended systems is central to describing many physical and biological systems that exhibit behaviour such as turbulence and wave propagation. Correctly predicting dynamics is advantageous in experimental settings and data-driven approaches are useful, particularly when no adequate mathematical models are available. We present an approach to iterated time series prediction of spatio-temporal dynamics based on local delay coordinate states and local modeling using nearest neighbour methods [1]. A crucial step in this process is to find predictive yet low-dimensional descriptions of the local dynamics . We discuss how imposing symmetries on the dynamics can be used to increase the predictiveness of our approach. The efficacy of this approach is shown for (noisy) data from a cubic Barkley model, the Bueno-Orovio-Cherry-Fenton model.
[1] J. Isensee, G. Datseris, U. Parlitz, J. of Nonlinear Sci. (2019)