Controlling dynamical systems to arbitrary target states using classical-, next-generation- and the new minimal reservoir computing

Kurzfassung

Utilizing machine learning to control nonlinear dynamical systems not only enables the imposition of simple behavior such as periodicity but also to drive the system into more intricate, arbitrary dynamics. The key lies in the machine learning system’s capacity to replicate the desired dynamics. To showcase this concept, we control a chaotic parametrization of the Lorenz system into intermittent dynamics. We start by employing classical reservoir computing (RC) and confirm its performance in this task. Subsequently, we conducted a comparative analysis with varying amounts of training data, benchmarking classical reservoir computing against next-generation reservoir computing as well as a newly presented approach called “minimal reservoir computing”. The latter is characterized by a simplified architecture, which is further minimizing computational resources. Our results demonstrate that, particularly in situations where data is scarce, both next-generation and minimal reservoir computing outperform classical reservoir computing, leading to a substantial enhancement in performance. In particular, the performance of minimal reservoir computing is comparable to next-generation reservoir computing. Given the advantages of minimal reservoir computing in the context of hardware implementations, this makes it an appealing choice for practical control applications in real-world scenarios with restricted access to data.