We analyze the modification of the computational properties of a time-delay photonic reservoir computer with a change in its feedback bandwidth. For a reservoir computing configuration based on a semiconductor laser subject to filtered optoelectronic feedback, we demonstrate that bandwidth selection can lead to a flat-topped eigenvalue spectrum for which a large number of system frequencies are weakly damped as a result of the attenuation of modulational instability by feedback filtering. This spectral configuration allows for the optimization of the reservoir in terms of its memory capacity, while its computational ability appears to be only weakly affected by the characteristics of the filter.

We provide a comprehensive analysis of the resonant properties of the memory capacity of a reservoir computer based on a semiconductor laser subjected to time-delayed filtered optoelectronic feedback. Our analysis reveals first how the memory capacity decreases sharply when the input-data clock cycle is slightly time-shifted from the time delay or its multiples. We attribute this effect to the inertial properties of the laser. We also report on the damping of the memory-capacity drop at resonance with a decrease of the virtual-node density and its broadening with the filtering properties of the optoelectronic feedback. These results are interpretated using the eigenspectrum of the reservoir obtained from a linear stability analysis. Then, we unveil an invariance in the minimum value of the memory capacity at resonance with respect to a variation of the number of nodes if the number is big enough and quantify how the filtering properties impact the system memory in and out of resonance.

We report experimentally and theoretically a dynamical scenario involving the formation of pulse multiplet structures, i.e., configurations of two, three, and more pulses per round trip, in a semiconductor laser with positive optoelectronic feedback. The delayed feedback loop includes a cascade of two band-limited amplifiers with nonlinear saturation of sigmoid type. The multiplets appear subcritically in the vicinity of the lasing threshold, resembling gain-switched operation, and evolve with the injection current.

The reservoir computing approach based on a semiconductor laser with optoelectronic time-delay feedback is distinguished by its simplicity, speed, and reliability. However, the response of the reservoir to the input signal in this configuration is a superposition of the laser relaxation oscillations, which has limited complexity, which may therefore reduce computational performance when solving problems requiring high nonlinearity. We experimentally demonstrate a combination of postprocessing techniques that overcome this limitation through upsampling and state space expansion using a nonlinear transformation of nodal functions, and show how this results in an order-of-magnitude reduction in prediction error for the Santa Fe task.

We examine a new design of reservoir computing based on an otherwise linear dynamical system subject to feedback in which a delay time linearly depends on the system's state. Despite the apparent linearity of the system under casual perusal, the system nonetheless possesses a nonlinearity that can be used for time-delay reservoir computing. We find that close multiple Hopf bifurcation points lead to a rich sawtooth-shaped transient response to input signals, which can be beneficial for computing capabilities. We benchmark the reservoir computing system's memory capacity and performance on solving delayed XOR, Iris flower classification tasks, and the Santa Fe time-series prediction task. We demonstrate how the nonlinearity and the memory capacity of the system can be tuned by changing the time-delay dependence.

In this theoretical study, we implement a reservoir computing system to simulate mass-to-charge ratio determination for a single trapped microparticle. To achieve this, we numerically obtained trajectory images of a single silica microparticle in a quadrupole ion trap in air at room temperature. We demonstrated the capacity of the RC system to distinguish both between different types of trajectories and within identical trajectory classes. The system quantified the mass-to-charge ratio of the particles with corresponding determination errors of approximately 7% and 10%.