Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networks

Abstract

Caused by finite signal propagation velocities, many complex systems feature time delays that may induce high-dimensional chaotic behavior and make forecasting intricate. Here, we propose an echo state network adaptable to the physics of systems with arbitrary delays. After training the network to forecast a system with a unique and sufficiently long delay, it already learned to predict the system dynamics for all other delays. A simple adaptation of the network's topology allows us to infer untrained features such as high-dimensional chaotic attractors, bifurcations, and even multistabilities, that emerge with shorter and longer delays. Thus, the fusion of physical knowledge of the delay system and data-driven machine learning yields a model with high generalization capabilities and unprecedented prediction accuracy.

Exploring the limits of multifunctionality across different reservoir computers

“…However, it has only recently been discovered that a given W out can enable a RC to perform more than one task. In this context, other than the results regarding multifunctionality, RCs have been trained to infer unseen attractors, learn global bifurcation structures and anticipate synchronisation [20]- [23].…”