Data-informed reservoir computing for efficient time-series prediction.

We propose a new approach to dynamical system forecasting called data-informed-reservoir computing (DI-RC) that, while solely being based on data, yields increased accuracy, reduced computational cost, and mitigates tedious hyper-parameter optimization of the reservoir computer (RC). Our DI-RC approach is based on the recently proposed hybrid setup where a knowledge-based model is combined with a machine learning prediction system, but it replaces the knowledge-based component by a data-driven model discovery technique. As a result, our approach can be chosen when a suitable knowledge-based model is not available. We demonstrate our approach using a delay-based RC as the machine learning component in conjunction with sparse identification of nonlinear dynamical systems for the data-driven model component. We test the performance on two example systems: the Lorenz system and the Kuramoto-Sivashinsky system. Our results indicate that our proposed technique can yield an improvement in the time-series forecasting capabilities compared with both approaches applied individually, while remaining computationally cheap. The benefit of our proposed approach, compared with pure RC, is most pronounced when the reservoir parameters are not optimized, thereby reducing the need for hyperparameter optimization.

Reservoir Computing with Delayed Input for Fast and Easy Optimisation.

Reservoir computing is a machine learning method that solves tasks using the response of a dynamical system to a certain input. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task-dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

Multipulse instabilities of a femtosecond SESAM-modelocked VECSEL.

Optically pumped passively modelocked vertical external-cavity surface-emitting lasers (VECSELs) can generate pulses as short as 100 fs with an intracavity semiconductor saturable absorber mirror (SESAM). Very stable soliton modelocking can be obtained, however, the high-Q-cavity, the short gain lifetime, and the kinetic-hole burning can also support rather complex multipulse instabilities which we analyze in more details here. This onset of multipulse operation limits the maximum average output power with fundamental modelocking and occurs at the roll-over of the cavity round trip reflectivity. Unfortunately, such multipulse operation sometimes can mimic stable modelocking when only limited diagnostics are available.

Multipulse dynamics of a passively mode-locked semiconductor laser with delayed optical feedback.

Passively mode-locked semiconductor lasers are compact, inexpensive sources of short light pulses of high repetition rates. In this work, we investigate the dynamics and bifurcations arising in such a device under the influence of time delayed optical feedback. This laser system is modelled by a system of delay differential equations, which includes delay terms associated with the laser cavity and feedback loop. We make use of specialised path continuation software for delay differential equations to analyse the regime of short feedback delays. Specifically, we consider how the dynamics and bifurcations depend on the pump current of the laser, the feedback strength, and the feedback delay time. We show that an important role is played by resonances between the mode-locking frequencies and the feedback delay time. We find feedback-induced harmonic mode locking and show that a mismatch between the fundamental frequency of the laser and that of the feedback cavity can lead to multi-pulse or quasiperiodic dynamics. The quasiperiodic dynamics exhibit a slow modulation, on the time scale of the gain recovery rate, which results from a beating with the frequency introduced in the associated torus bifurcations and leads to gain competition between multiple pulse trains within the laser cavity. Our results also have implications for the case of large feedback delay times, where a complete bifurcation analysis is not practical. Namely, for increasing delay, there is an ever-increasing degree of multistability between mode-locked solutions due to the frequency pulling effect.

Suppression of Noise-Induced Modulations in Multidelay Systems.

Many physical systems involve time-delayed feedback or coupling. In such delay systems, noise can give rise to undesirable oscillations at frequencies resonant to the delay times. We investigate how an additional feedback term can suppress noise-induced modulations in delay systems with self-feedback that exhibit deterministic oscillatory dynamics. A simple characteristic equation is derived to predict optimal delay times for the prototypical example of a Stuart-Landau oscillator subject to two feedback terms. We then show that a characteristic equation of the same form accurately describes the dominant Floquet modes of more complex oscillatory systems and hence can be used to optimize the suppression of noise-induced modulations. This is shown for mode-locked lasers and FitzHugh-Nagumo oscillators subject to self-feedback.

Dynamics of a passively mode-locked semiconductor laser subject to dual-cavity optical feedback.

We study the influence of dual-cavity optical feedback on the emission dynamics and timing stability of a passively mode-locked semiconductor laser using a delay differential equation model and verify the timing stability results by an initial experiment. By bifurcation analysis in dependence of the feedback delay times and feedback strength bistability, quasiperiodic and chaotic dynamics, as well as fundamental mode-locking are investigated, yielding a comprehensive overview on the nonlinear emission dynamics arising due to dual-cavity optical feedback. Optimum self-locking ranges for improving the timing stability by dual-cavity optical feedback are identified. A timing jitter reduction and an increase of the repetition rate tuning range of up to a factor of three, compared with single-cavity feedback, are predicted for the parameter ranges investigated. Improved timing stability on short and long timescales is predicted for dual-cavity feedback through the suppression of noise-induced fluctuations. Based on the numerical predictions, experimentally, a maximum timing jitter reduction up to a factor of 180 is found, accompanied by a side-band reduction by a factor of 58 dB, when both feedback cavities are resonant.