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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]

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]