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

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.