Dynamics and learning in complex networks of nanomechanical oscillators

Understanding and harnessing dynamics and pattern formation in high-dimensional nonlinear systems is key to unlocking the physics of numerous natural and engineered systems. The theoretical and computational literature has explored the topic deeply, particularly regarding networks of coupled limit cycle oscillators reduced to a phase-only description. In contrast, experiments have lagged far behind. Top-down studies are often limited by readout and control, and bottom-up construction of such networks is challenging and engineering intensive. To-date, real-world experiments have only examined a small slice of the parameter space available, leaving much of existing analytical work untested. To address this, we developed a platform based on piezoelectric nano-electro-mechanical systems (NEMS) resonators with electronic feedback and coupling to build highly controllable and reconfigurable networks permitting everything relevant to be measured in detail. NEMS are an ideal candidate for such experiments because they have wide ranging dynamical timescales (kHz to GHz), excellent tunability, strongly nonlinear vibrations, low power dissipation, and massive scalability via integration with complementary metal-oxide-semiconductor (CMOS) technology. In this talk, I will review the underlying physics of our experimental paradigm and results from studying the dynamics on a ring of 8 oscillators with nearest neighbor coupling. In these experiments, we discovered numerous exotic states emerging from relevant multi-body interactions in the higher order phase dynamics. In this presentation, our recent effort on extending the experimental platform to enable programming and control of 8-node network topologies will be reviewed. I will conclude by discussing our numerical and analytical efforts to study the information processing capacity of NEMS oscillator networks by using them for physical reservoir computing. This demonstrates the potential for analog computing with NEMS and illuminates the practical requirements.