Parameters optimization method for the time-delayed reservoir computing with a nonlinear duffing mechanical oscillator

Abstract

Reservoir computing (RC) is a recently introduced bio-inspired computational framework capable of excellent performances in the temporal data processing, owing to its derivation from the recurrent neural network (RNN). It is well-known for the fast and effective training scheme, as well as the ease of the hardware implementation, but also the problematic sensitivity of its performance to the optimizable architecture parameters. In this article, a particular time-delayed RC with a single clamped–clamped silicon beam resonator that exhibits a classical Duffing nonlinearity is presented and its optimization problem is studied. Specifically, we numerically analyze the nonlinear response of the resonator and find a quasi-linear bifurcation point shift of the driving voltage with the driving frequency sweeping, which is called Bifurcation Point Frequency Modulation (BPFM). Furthermore, we first proposed that this method can be used to find the optimal driving frequency of RC with a Duffing mechanical resonator for a given task, and then put forward a comprehensive optimization process. The high performance of RC presented on four typical tasks proves the feasibility of this optimization method. Finally, we envision the potential application of the method based on the BPFM in our future work to implement the RC with other mechanical oscillators.

Processing IMU action recognition based on brain-inspired computing with microfabricated MEMS resonators

“…To illustrate the differences between systems, normalized mean square error (NMSE = 2 /var(y)) is used to measure system performance. The BPFM(bifurcation point frequency modulation) method discussed in detail in studies [32] is used to find the operating point of the system and determine the order of adjustment parameters. In this experiment, the drive frequency of resonators equals f d = 253 000 Hz and the DC bias voltage equals V dc = 10 V, while AC drive voltage equals V ac = 1.4 V. Since this data set is relatively simple, sufficiently high accuracy can be achieved without a lot of virtual nodes.…”

“…Hardware RC system requires two crucial properties, multi-dimensional nonlinear mapping ability and memory capacity that can memorize data a few steps or tens of steps ago. Due to its excellent Duffing nonlinear performance and suitable attenuation characteristics, MEMS resonators are appropriate as the nonlinear node of the hardware reservoir system [31,32]. Most of the prediction and classification tasks processed by hardware RC are based on the general data sets, such as parity benchmark [30], nonlinear autoregressive moving average (NARMA) task [13,33,34], Santa Fe laser [26,35,36], Mackey-Glass time-series tasks [35], nonlinear channel equalization benchmark task [37,38], signal classification [18,26], isolated word recognition [13,18,30], video action recognition [34,39], and handwritten digit classification [20,40].…”

A Hopf physical reservoir computer

“…The echo state architecture of a reservoir allows the use of physical systems as reservoir computers, also known as physical reservoir computers (PRCs). Many physical systems have been shown to perform as PRCs, including an array of nonlinear mechanical oscillators 11 , 22 , 23 , soft robotic bodies 20 , 24 – 26 , tensegrity structures 21 , 27 , and origami structures 28 , 29 .…”

Reservoir Computing with Delayed Input for Fast and Easy Optimization

“…25 However, even when these criteria are fulfilled, the performance depends greatly on the 26 dynamics of the reservoir. Hence, in the past two decades a lot of research in the reservoir 27 computing community has focused on the optimisation of the reservoir parameters [3][4][5][6][7][8][9]. 28 Furthermore, the optimisation of the reservoir is a task specific problem [1,[10][11][12] and a 29 universal reservoir, which performs well on a range of tasks, remains elusive.…”