Predicting synchronization and oscillation death with parallel reservoir computing

Reservoir computing has emerged as a powerful framework for predicting critical transitions in dynamical systems. In this work, we employ parallel parameter-aware reservoir computing to predict the dynamics of multilayer networks with distinct coupling mechanisms. We consider a two-layer multiplex network in which the first layer oscillators are coupled with attractive coupling, which promotes in-phase synchronization, while the second layer oscillators are coupled with repulsive coupling, encouraging anti-phase synchronization and oscillation death. With sufficiently strong interlayer coupling, collective emergent phenomena can be transferred from one layer to another. Notably, we also observe that interlayer coupling can induce oscillation death simultaneously in both layers. Using a parallel parameter-aware reservoir computing scheme, we accurately predict the critical parameter values at which the transfer of dynamical phenomenon occurs. We use two reservoirs designated to learn the dynamics of each layer in a two-layer multiplex network. Our findings provide valuable insight into the role of reservoir computing in forecasting transitions in multilayer networks.