Constructive Role of Noise for High-Quality Replication of Chaotic Attractor Dynamics Using a Hardware-Based Reservoir Computer

Abstract

Hardware-implemented reservoir computing (RC) has been gaining considerable interest in recent years, in particular for classification and nonlinear-prediction tasks. Such RC systems often perform analog computation and, therefore, may be more sensitive to noise than digital systems; noise has been found to often degrade the computational performance. In contrast, here we demonstrate that noise can also play a constructive role in hardware-based RC. Using a hybrid delay-based RC system with an analog part (nonlinearity) and a digital part, we show that the replication of chaotic attractor dynamics is overall improved when the reservoir is trained with an input signal modified by additive Gaussian noise. To quantify the performance of the attractor replication, we suggest two different methods based on recurrence plots and power spectra.

Chaotic time series prediction by noisy echo state network

“…Recently, Estébanez et al conducted an experiment on the nonlinear forecasting of chaotic time series generated by the Rössler equations using a hardware-implemented reservoir computer. They reported that the addition of external noise to the reservoir network was effective for improving the degree of fidelity of the Rössler attractor reconstructed from the predicted time series, although they did not discuss their experimental results in terms of Ueda's theory of chaos [9]. Similar results obtained using a photonic reservoir computer were reported by Antonik et al [5].…”

“…Reservoir computing is a new approach to constructing recurrent neural networks. In particular, the echo state network (ESN) is a practical method for implementing a reservoir computer [1][2][3] and has been shown to be effective, for example, for chaotic time series prediction [4][5][6][7][8][9][10]. When applied to time series prediction, the ESN usually has three layers, i.e., the input layer consisting of a single node from which input data are generated, the reservoir layer consisting of sparsely coupled multiple nodes (reservoir network), and the output layer consisting of a single node from which predicted values are provided.…”

Transfer learning for nonlinear dynamics and its application to fluid turbulence

“…Although the present study focused on the nonlinear dynamics, transfer learning for RC is a model-free flexible ML-method, and hence, can be applied to any other physical system. Physical RC, physical implementations of RC using physical devices such as lasers, is highly active research topic [18][19][20], and the transfer learning is also useful to realize the physical RC.…”

Reconfigurable FPGA Realization of Fractional-Order Chaotic Systems

“…This generic FPGA system can realize many fractional-order applications on hardware, e.g., edge detection [38], [39], control [40], [41], synchronization [42] and encryption [43]. Additionally, it can replace the current realizations of mixed-signal and digitally implemented fractional-order applications with the reconfigurable one, e.g., analog/mixed-signal systems [44], [45], control [46] and encryption [12], [47]- [49]. Furthermore, it can be used in variable-order chaotic systems [50], [51], dynamic switching and synchronization [52], and encryption applications with dynamic encryption key [53].…”