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We analyse the memory capacity of a delay-based reservoir computer with a Hopf normal form as nonlinearity and numerically compute the linear as well as the higher order recall capabilities. A possible physical realization could be a laser with external cavity, for which the information is fed via electrical injection. A task-independent quantification of the computational capability of the reservoir system is done via a complete orthonormal set of basis functions. Our results suggest that even for constant readout dimension the total memory capacity is dependent on the ratio between the information input period, also called the clock cycle, and the time delay in the system. Optimal performance is found for a time delay about 1.6 times the clock cycle. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The dynamical properties of an optical neuron formed by a quantum dot semiconductor laser model subjected to optical injection and optical feedback are analyzed. The parameter space spanned by the injection strength and frequency detuning of the optical injection is systematically scanned and modulations of the bifurcation boundaries that induce complex scenarios are found, which enable new opportunities to introduce the optical setup as an optical neuron. The counterintuitive behavior of coherence resonance for different setups of a single‐driven optical neuron under optical feedback is also found. Following the results, the microscopically motivated quantum dot laser rate equation model is reduced to the normal form of a saddle‐node infinite period (SNIPER) bifurcation for low injection strengths and a network of four such SNIPER systems in a globally coupled setup is studied. A new phenomenon is observed, which is called collective coherence resonance. This novel dynamical behavior is connected to the coexistence of a network‐wide SNIPER bifurcation and a change in stability for the synchronized manifold, analyzed via the master stability function. [ABSTRACT FROM AUTHOR]

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The deep time-delay reservoir computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity (MC) and how that can be used for optimization. In particular, we analyze bifurcations of the corresponding autonomous system and compute conditional Lyapunov exponents, which measure generalized synchronization between the input and the layer dynamics. We show how the MC is related to the systems' distance to bifurcations or magnitude of the conditional Lyapunov exponent. The interplay of different dynamical regimes leads to an adjustable distribution between the linear and nonlinear MC. Furthermore, numerical simulations show resonances between the clock cycle and delays of the layers in all degrees of MC. Contrary to MC losses in single-layer reservoirs, these resonances can boost separate degrees of MC and can be used, e.g., to design a system with maximum linear MC. Accordingly, we present two configurations that empower either high nonlinear MC or long time linear MC. [ABSTRACT FROM AUTHOR]

We experimentally and analytically investigate the influence of temperature on the linewidth of an InP quantum dot (QD) laser. The full width half maximum of the peak in the optical spectrum strongly depends on the pump current and rebroadens at high injection levels. We show that with increasing temperature these effects are amplified. Applying a QD laser model including the excited and ground state with detailed balance scattering rates, we are capable of reproducing the experimentally observed data qualitatively and thus show that a relatively simple QD-laser model is capable of capturing this complex behavior. Additionally, we include a temperature dependent energy band gap reduction needed to fit the data and show that this effect enhances the rebroadening effect for higher temperatures. [ABSTRACT FROM AUTHOR]

Parcel services route vehicles to pick up parcels in the service area. Pickup requests occur dynamically during the day and are unknown before their actual request. Because of working hour restrictions, service vehicles only have a limited time to serve dynamic requests. As a result, not all requests can be confirmed. To achieve an overall high number of confirmed requests, dispatchers have to budget their time effectively by anticipating future requests. To determine the value of a decision, i.e., the expected number of future confirmations given a point of time and remaining free time budget, we present an anticipatory time budgeting heuristic (ATB) drawing on methods of approximate dynamic programming. ATB frequently simulates a problem's realization to subsequently approximate the values for every vector of point of time and free time budget to achieve an approximation of an optimal decision policy. Since the number of vectors is vast, we introduce the dynamic lookup table (DLT), a general approach adaptively partitioning the vector space to the approximation process. Compared with state-of-the-art benchmark heuristics, ATB allows an effective use of the time budget resulting in anticipatory decision making and high solution quality. Additionally, the DLT significantly strengthens and accelerates the approximation process. [ABSTRACT FROM AUTHOR]

Mathematical modelling reveals: Quantum‐dot lasers behave like optical neurons and show coherence resonance. – A collaboration between TU Berlin and University College Cork analyzed the influence of optical injection and feedback with delay in a microscopically motivated quantum‐dot model. Coupled together, various synchronization patterns of noise‐induced spiking emerged. The stability of these dynamical patterns has been systematically investigated in dependence on the injection strength and detuning between the lasers. The coupling delay induces regions where complex dynamics emerges and neuron‐like behavior can be found. For further details, see article number 2100345 by Kathy Lüdge and co‐workers. [ABSTRACT FROM AUTHOR]

The stability of these dynamical patterns has been systematically investigated in dependence on the injection strength and detuning between the lasers. Mathematical modelling reveals: Quantum-dot lasers behave like optical neurons and show coherence resonance. - A collaboration between TU Berlin and University College Cork analyzed the influence of optical injection and feedback with delay in a microscopically motivated quantum-dot model. [Extracted from the article]