Theoretical analysis of physical reservoir computing using spin waves

Reservoir computing (RC) is a variant of recurrent neural networks (RNNs), which has a single reservoir layer to transform an input signal into an output. In contrast with the conventional RNNs, RC does not update the weights in the reservoir. Therefore, by replacing the reservoir with a physical system, for example, magnetization dynamics, we may realize a neural network device to perform various tasks. A key issue to improve its performance is how to increase a reservoir dimension to memorize a lot of information. Wave-based computational systems have attractive features in this direction because the dynamics in the continuum media have inherently large degrees of freedom. Among the wave phenomena, spin waves are promising for high-speed nanoscale devices. However, the realization of high-performance computation has not yet been achieved.



Here we show, using reservoir computing with micromagnetic simulations, that spin-wave physical reservoir computing can achieve high computational power comparable with other state-of-art systems. We demonstrate the performance by memory capacity, information processing capacity, which is a nonlinear version of the memory capacity, NARMA10 task, and forecasting chaotic time series. We analyze the response function perturbatively, and clarify the mechanism of high computational performance in terms of the geometry and the number of input nodes and physical parameters.