Multivariate nonlinear time-series estimation using delay-based reservoir computing

Multivariate nonlinear time-series analysis represents a major challenge in complex systems science, specially when the full underlying dynamics is unknown. Often, time-series forecast relies on the information contained in a single measured variable. However, in many cases one might benefit from other available measures of the system to improve the prediction of its dynamical evolution. Here, we utilize Reservoir Computing techniques to process sequential multivariate information. As reservoir, we employ a Mackey-Glass delay system. We discuss the approximation of a three-dimensional theoretical model (the Lorenz model) by comparing prediction performance for one variable using either one or two variables as input. Finally, we apply these insights to improve the performance of a relevant biomedical task, namely multi-electrode heartbeat classification.