Neuromorphic Computing Based on Parametrically-Driven Oscillators and Frequency Combs

TL;DR

This paper demonstrates that parametrically driven oscillators operating in the parametric resonance regime can serve as effective reservoir computers for predicting chaotic systems, with performance influenced by system parameters.

Contribution

It identifies parametric resonance as a robust regime for oscillator-based reservoir computing and offers design principles for optimizing neuromorphic systems.

Findings

Optimal prediction performance occurs in the parametric resonance regime.

Frequency-comb states increase spectral dimensionality but do not always improve performance.

Prediction accuracy correlates with bifurcation structure and dynamical regimes.

Abstract

Parametrically driven oscillators provide a natural platform for neuromorphic computation, where nonlinear mode coupling and intrinsic dynamics enable both memory and high-dimensional transformation. Here, we investigate a two-mode system exhibiting 2:1 parametric resonance and demonstrate its operation as a reservoir computer across distinct dynamical regimes, including sub-threshold, parametric resonance, and frequency-comb states. By encoding input signals into the drive amplitude and sampling the resulting temporal and spectral responses, we perform one step-ahead prediction of benchmark chaotic systems, including Mackey-Glass, Rossler, and Lorenz dynamics. We find that optimal computational performance is achieved within the parametric resonance regime, where nonlinear interactions are activated while temporal coherence is preserved. In contrast, although frequency-comb states introduce increased spectral dimensionality, their performance is not consistently good across their existence band and also degrades in the chaotic comb regime due to loss of phase coherence. Mapping prediction error over parameter space reveals a direct correspondence between computational capability and the underlying bifurcation structure, with low-error regions aligned with the parametric resonance boundary. We further show that the input modulation, the detuning from the frequency matching condition, damping ratio, and input data rate systematically control the accessible dynamical regimes and thereby the computational performance. These results establish parametric resonance as a robust operating regime for oscillator-based reservoir computing and provide design principles for tuning physical systems toward optimal neuromorphic functionality.