Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 58: Poster: Nonlinear Dynamics; Pattern Formation; Networks; Delay Systems; Synchronization
DY 58.16: Poster
Thursday, March 19, 2020, 15:00–18:00, P1C
Deep Time-Delay Reservoir Computing: Dynamics and Memory Capacity — •Mirko Goldmann1, Kathy Lüdge1, and Serhiy Yanchuk2 — 1Institute of Theoretical Physics, Technische Universität Berlin, D-10623, Germany — 2Institute of Mathematics, Technische Universität Berlin, D-10623, Germany
The success of single node delay-based Reservoir Computer for time-series prediction has triggered interest in more complex network architectures [1, 2, 3]. Inspired by the recently introduced optoelectronic setup by Penkovsky et al. [1], we present the concept of Deep Time-Delay Reservoir Computer (DTRC) consisting of unidirectionally connected layers with time-delay loops.
First, we analytically investigate the dynamical properties of the autonomous DTRC based on the Ikeda system. The stability of the autonomous system is related to the numerically computed conditional Lyapunov exponent of the driven DTRC. We can show that adding layers to the DTRC increases the Lyapunov exponent while preserving the stability. Further, we explain the relation between the linear and nonlinear Memory Capacities (MC), Lyapunov exponents, and the layer's read-out weights.
In a second step we study the recently reported resonances between the clock cycle time and the lengths of the delays [4]. Numerical simulations show these resonances in all layers and in different degrees of the MC. In contrast to the single node case reported in [4], the resonances in deeper layers can increase the MC. Further, we show that varying the delays in single layers enables balancing between the linear and nonlinear MC.
[1] B. Penkovsky, X. Porte, M. Jacquot, L. Larger, and D. Brunner, Physical Review Letters 123 (2019), 1902.05608.
[2] A. Röhm and K. Lüdge, Journal of Physics Communications 2, 085007 (2018).
[3] Y. Chen, L. Yi, J. Ke, Z. Yang, Y. Yang, L. Huang, Q. Zhuge, and W. Hu, Optics Express 27, 27431 (2019).
[4] F. Stelzer, A. Röhm, K. Lüdge, and S. Yanchuk, Neural Networks 124, 158 (2019), 1905.02534.