Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing
This work addresses control of nonlinear dynamical systems for applications in real-world problems where data availability is restricted, representing an incremental improvement over existing methods.
The study tackled controlling a chaotic Lorenz system to achieve complex intermittent dynamics using machine learning, finding that next-generation reservoir computing significantly outperforms classical reservoir computing when training data is very limited, with comparable performance under normal data conditions.
Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be trained to reproduce the target dynamics sufficiently well. On the example of forcing a chaotic parametrization of the Lorenz system into intermittent dynamics, we show first that classical reservoir computing excels at this task. In a next step, we compare those results based on different amounts of training data to an alternative setup, where next-generation reservoir computing is used instead. It turns out that while delivering comparable performance for usual amounts of training data, next-generation RC significantly outperforms in situations where only very limited data is available. This opens even further practical control applications in real world problems where data is restricted.