Publications

We used reservoir computing to explore the changes in the connectivity patterns of whole-brain anatomical networks derived by diffusion-weighted imaging, and their impact on cognition during aging. The networks showed optimal performance at small densities. This performance decreased with increasing density, with the rate of decrease being strongly associated with age and performance on behavioural tasks measuring cognitive function. This suggests that a network core of anatomical hubs is crucial for optimal functioning, while weaker connections are more susceptible to aging effects. This study highlights the potential utility of reservoir computing in understanding age-related changes in cognitive function.

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.

We investigate the spontaneous emission noise resilience of the phase-locked operation of two delay-coupled nanolasers. The system is modeled by semi-classical Maxwell-Bloch rate equations with stochastic Langevin-type noise sources. Our results reveal that a polarization dephasing time of two to three times the cavity photon lifetime maximizes the system’s ability to remain phase-locked in the presence of noise-induced perturbations. The Langevin noise term is caused by spontaneous emission processes which change both the intensity auto-correlation properties of the solitary lasers and the coupled system. In an experimental setup, these quantities are measurable and can be directly compared to our numerical data. The strong parameter dependence of the noise tolerance that we find may show possible routes for the design of robust on-chip integrated networks of nanolasers.

In the reservoir computing literature, the information processing capacity is frequently used to characterize the computing capabilities of a reservoir. However, it remains unclear how the information processing capacity connects to the performance on specific tasks. We demonstrate on a set of standard benchmark tasks that the total information processing capacity correlates poorly with task specific performance. Further, we derive an expression for the normalized mean square error of a task as a weighted function of the individual information processing capacities. Mathematically, the derivation requires the task to have the same input distribution as used to calculate the information processing capacities. We test our method on a range of tasks that violate this requirement and find good qualitative agreement between the predicted and the actual errors as long as the task input sequences do not have long autocorrelation times. Our method offers deeper insight into the principles governing reservoir computing performance. It also increases the utility of the evaluation of information processing capacities, which are typically defined on i.i.d. input, even if specific tasks deliver inputs stemming from different distributions. Moreover, it offers the possibility of reducing the experimental cost of optimizing physical reservoirs, such as those implemented in photonic systems.

Passively mode-locked semiconductor disk lasers have received tremendous attention from both science and industry. Their relatively inexpensive production combined with excellent pulse performance and great emission-wavelength flexibility make them suitable laser candidates for applications ranging from frequency-comb tomography to spectroscopy. However, due to the interaction of the active medium dynamics and the device geometry, emission instabilities occur at high pump powers and thereby limit their performance potential. Hence, understanding those instabilities becomes critical for an optimal laser design. Using a delay-differential equation model, we are able to detect, understand, and classify three distinct instabilities that limit the maximum achievable pump power for the fundamental mode-locking state and link them to characteristic positive-net-gain windows. We furthermore derive a simple analytic approximation in order to quantitatively describe the stability boundary. Our results enable us to predict the optimal laser-cavity configuration with respect to positive-net-gain instabilities and therefore may be of great relevance for the future development of passively mode-locking semiconductor disk lasers.