  Physical Reservoir Computing (PRC) is a recently developed variant of
Neuromorphic Computing, where a pertinent physical system effectively projects
information encoded in the input signal into a higher-dimensional space. While
various physical hardware has demonstrated promising results for Reservoir
Computing (RC), systems allowing tunability of their dynamical regimes have not
received much attention regarding how to optimize relevant system parameters.
In this work we employ hybrid photonic-electronic (HPE) system offering both
parallelism inherent to light propagation, and electronic memory and
programmable feedback allowing to induce nonlinear dynamics and tunable
encoding of the photonic signal to realize HPE-RC. Specifically, we
experimentally and theoretically analyze performance of integrated silicon
photonic on-chip Mach-Zehnder interferometer and ring resonators with heaters
acting as programmable phase modulators, controlled by detector and the
feedback unit capable of realizing complex temporal dynamics of the photonic
signal. Furthermore, we present an algorithm capable of predicting optimal
parameters for RC by analyzing the corresponding Lyapunov exponent of the
output signal and mutual information of reservoir nodes. By implementing the
derived optimal parameters, we demonstrate that the corresponding resulting
error of RC can be lowered by several orders of magnitude compared to a
reservoir operating with randomly chosen set of parameters.
