Dresden 2017 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Complex Systems

DY 13.3: Vortrag

Montag, 20. März 2017, 18:00–18:15, ZEU 147

An Equal Space: Data-driven Embedding of Complex Dynamics — •Felix Kemeth^1,2, Sindre W. Haugland^1,2, Yannis Kevrekidis^2,3, and Katharina Krischer¹ — ¹Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching, Germany — ²Institute for Advanced Study - Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching, Germany — ³The Department of Chemical and Biological Engineering - Princeton University, Princeton, NJ 08544, USA

We present a way to embed nonlinear phenomena in a meaningful and low-dimensional space. In particular we apply diffusion maps, a non-linear dimensionality reduction method, to extract useful axes from measurements or simulation data of different non-linear phenomena. Useful hereby refers to the degree of coarsening in which we want to observe our system, with this degree being specified by appropriately tuning the kernel scale in the diffusion maps approach. In addition, we demonstrate that these axes are, provided we have sufficient data, independent of the particular nature of the measurement entity. As illustrative examples, we apply our method on spatio-temporal chaotic dynamics apparent in the complex Ginzburg-Landau equation, on modulated traveling waves in the Kuramoto-Sivashinksy equation and on chimera states, states of coexisting coherence and incoherence. For the latter, we show that it is possible to extract insightful order parameters, allowing further understanding of these intricate dynamics.