Coupled Microelectromechanical Drum Resonators for Reservoir Computing via Sideband Pumped Phonon-Cavity Dynamics

TL;DR

This paper demonstrates a compact MEMS-based physical reservoir computing platform built from two capacitively coupled drums operating in the MHz range. By employing a blue sideband pump in a phonon-cavity electromechanical scheme and a time-delay feedback loop, nonlinear energy transfer between the coupled modes is harnessed to realize a robust reservoir. The authors evaluate performance with parity and NARMA benchmarks, showing strong short-term nonlinear memory and identifying limitations due to fast Al-mode decay and MHz-scale fading memory, while highlighting the method’s potential for multimode sensing-and-computing integration. The work suggests a scalable route to multimode MEMS/optomechanical reservoir architectures with low energy per input and dense integration.

Abstract

Reservoir computing is a bio-inspired machine learning paradigm that exploits the intrinsic dynamics of nonlinear systems with fading memory for efficient temporal information processing. Microelectromechanical resonators offer a promising platform for reservoir computing as they inherently possess the requisite nonlinear and temporal properties while also facilitating the integration of sensing and computing within a single platform. In this work, we experimentally demonstrate a physical reservoir computing platform based on two capacitively coupled drum resonators, operating in the MHz frequency regime. Taking advantage of the concept of phonon-cavity electromechanics, a pump tone is applied at the sideband of the phonon cavity while probing one of the coupled modes, analogous to optomechanical systems, thereby creating nonlinear dynamics in energy transfer between the two resonators. Physical reservoir computing is implemented by exploiting the nonlinear response induced through pump amplitude modulation in combination with a time-delay feedback loop, and the performance is evaluated using both parity and Normalized Auto-Regressive Moving Average benchmarks. This work demonstrates a compact microelectromechanical platform for the integration of sensing and reservoir computing. Moreover, the sideband pumping scheme can further extend conventional single resonator reservoir computing to a multimode architecture.

Figures (5)

• Figure 1: Experiment setup. (a) Optical image of the Al drum resonator which is suspended over the SiN circular drum by the means of 4 support feet. (b) Optical image of the bottom SiN membrane resonator, covered with an Al thin film. There is no physical connection between the two drums. (c) Cross sectional view of the electromechanical system. (d) and (f) The mechanical responses of the SiN and Al drum resonators are measured under a $DC$ bias of $V_{dc}$ = 4 V, with $AC$ drive of $V_{d}$ = 6 mV and 80 mV, respectively, each attenuated by 20 dB. The red lines represent the Lorentz fitting result. (e) Schematic diagram of the measurement setup. The mechanical displacement is read out using a lock-in amplifier via microwave optomechanical interferometry. The output of the FPGA is used to modulate the pump signal through a multiplier.
• Figure 2: Diagram of the blue sideband pumping scheme while probing (a) the phonon-cavity SiN drum and (b) the Al membrane resonator, respectively. (c) The measured normalized mechanical responses as a function of the pump amplitude. The background contribution has been subtracted using the measured minimum amplitude as a reference. The black (red) curve is measured by probing Al (SiN) drum at $\Omega_d/(2\pi)$ = 6.12 MHz ( = 12.25 MHz) with amplitude $V_d$ = 80 mV (6 mV) attenuated by 20 dB, with $\Omega_p/(2\pi)$ = 18.38 MHz and $V_{dc}$ = 4 V. (d) Analytical calculation results of the mechanical amplitude as a function of the pump amplitude in both probing cases, by using experimental parameters. (e) Schematic of the concept for implementing reservoir computing in coupled drum resonators.
• Figure 3: Reservoir computing based on the sideband pumping mechanism while probing the SiN drum with $\Omega_d/(2\pi) = 12.26$ MHz, $V_{d} = 6$ mV attenuated by 20 dB, $\Omega_p/(2\pi) = 18.38$ MHz and $V_{dc} = 4$ V. (a) The detected mechanical displacement of the probed SiN membrane as a function of the amplitude of the blue pump signal. The curve is divided into 4 modulation windows $M1$, $M2$, $M3$, and $M4$ showcasing different profile variations depending on the interval of the blue pump voltage. (b) Comparison between the predicted output by our reservoir computing scheme (black lines) and the target ideal output of the parity benchmark (red lines) for the first 7 orders of the parity benchmark in the case of the modulation window $M4$. (c) Success rates obtained for the first 4 orders of the parity benchmark corresponding to each of the 4 modulation windows.
• Figure 4: Reservoir computing based on the sideband pumping mechanism while probing the Al drum with $\Omega_d/(2\pi) = 6.12$ MHz, $V_{d} = 80$ mV (before a 20 dB attenuation), $\Omega_p/(2\pi) = 18.38$ MHz and $V_{dc} = 4$ V. (a) The detected mechanical displacements of the probed Al membrane as a function of the variation of the amplitude of the blue pump signal. The curve is divided into three modulation windows of the pump amplitudes the $M1$, $M2$ and $M3$ where the detected probe tone exhibits different variations. (b) Success rates for the first four orders of the parity benchmark (from $P_1$ to $P_4$) for the three different modulation windows. (c) The values of the obtained NMSE in the case of testing NARMA2 and NARMA10 tasks, corresponding to each pump force modulation window shown in the (a).
• Figure 5: The obtained NMSE values as a function of the order of the NARMA Benchmark in the case of (a) Duffing nonlinearity, and blue sideband pumping the phonon-cavity while (b) probing the SiN drum (c) probing the Al drum.