Reservoir computing is a machine learning approach to designing artificial neural networks. Despite the significant simplification of the training process, the performance of such systems is comparable to other digital algorithms on a series of benchmark tasks. Recent investigations have demonstrated the possibility of performing long-horizon predictions of chaotic systems using reservoir computing. In this work we show that a trained reservoir computer can reproduce sufficiently well the properties a chaotic system, hence allowing full synchronisation. We illustrate this behaviour on the Mackey-Glass and Lorenz systems. Furthermore, we show that a reservoir computer can be used to crack chaos-based cryptographic protocols and illustrate this on two encryption schemes.

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals (Jaeger andHaas 2004; Maass, Natschläger, and Markram 2002). It canbe easily implemented in hardware. The performance ofthese analogue devices matches digital algorithms on a series of benchmark tasks (see e.g. (Soriano et al. 2015) fora review). Their capacities could be extended by feedingthe output signal back into the reservoir, which would allow them to be applied to various signal generation tasks(Antonik et al. 2016b). In practice, this requires a high-speed readout layer for real-time output computation. Herewe achieve this by means of a field-programmable gate array (FPGA), and demonstrate the first photonic reservoircomputer with output feedback. We test our setup on theMackey-Glass chaotic time series generation task and obtain interesting prediction horizons, comparable to numerical simulations, with ample room for further improvement.Our work thus demonstrates the potential offered by the output feedback and opens a new area of novel applications forphotonic reservoir computing.

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals. It can be easily implemented in hardware. The performance of these analogue devices matches digital algorithms on a series of benchmark tasks. Their capacities could be extended by feeding the output signal back into the reservoir, which would allow them to be applied to various signal generation tasks. In practice, this requires a high-speed readout layer for real-time output computation. Here we achieve this by means of an FPGA chip, and demonstrate the first photonic reservoir computer with output feedback. We test our setup on the Mackey-Glass chaotic time series generation task and obtain interesting prediction horizons, comparable to numerical simulations, with ample room for further improvement. Our work thus demonstrates the potential offered by the output feedback and opens a new area of novel applications for photonic reservoir computing.

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. The performance of its analog implementation is comparable to other state-of-the-art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here, we investigated the online learning approach by training an optoelectronic reservoir computer using a simple gradient descent algorithm, programmed on a field-programmable gate array chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analog devices to equalize the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well suited for realistic channel equalization by testing it on a drifting and a switching channel and obtaining good performances.