Extrapolating learned dynamics across bifurcations based on generalized synchronization

Overview & Synopsis

Predicting dynamics across bifurcations by extrapolating trained models is crucial in diverse fields of physics. Generalized synchronization provides a framework for understanding dynamical reconstruction by neural networks, especially in the context of reservoir computing. Building on this framework, we derive a formula combining pretrained readouts to reconstruct unseen chaotic dynamics. Using classical Lagrange interpolation theory, we derive rigorous bounds on readout errors and conjugacy residuals. Numerical examples demonstrate accurate prediction of chaotic dynamics across bifurcations.