Rok Cestnik

Rok Cestnik, Erik A. Martens

We present a simple and scalable implementation of next-generation reservoir computing for modeling dynamical systems from time series data. Our approach uses a pseudorandom nonlinear projection of time-delay embedded input, allowing an arbitrary dimension of the feature space, thus providing a flexible alternative to the polynomial-based projections used in previous next-generation reservoir computing variants. We apply the method to benchmark tasks -- including attractor reconstruction and bifurcation diagram estimation -- using only partial and noisy observations. We also include an exploratory example of estimating asymptotic oscillation phases. The models remain stable over long rollouts and generalize beyond training data. This framework enables the precise control of system state and is well suited for surrogate modeling and digital twin applications.

Rok Cestnik, Markus Abel

We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system, but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay and chaotic systems. Furthermore, with a statistical analysis we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit.