Dynamical analysis of a parameter-aware reservoir computer

Reservoir computing is a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. This work shows how the dynamical system theory provides the underlying mechanism behind the prediction. Using numerical methods, by considering dynamical systems which show Hopf bifurcation, we demonstrate that the map produced by the reservoir after a successful training undergoes a Neimark-Sacker bifurcation such that the critical point of the map is in immediate proximity to that of the original dynamical system. Also, we compare and analyze how the framework learns to distinguish between different structures in the phase space. Our findings provide insight into the functioning of machine learning algorithms for predicting critical transitions.