Robust prediction of complex spatiotemporal states through machine learning with sparse sensing

Complex spatiotemporal states arise frequently in material as well as biological systems consisting of multiple interacting units. A specific, but rather ubiquitous and interesting example is that of “chimeras”, existing in the edge between order and chaos. We use Machine Learning methods involving “observers” to predict the evolution of a system of coupled lasers, comprising turbulent chimera states and of a less chaotic biological one, of modular neuronal networks containing states that are synchronized across the networks. We demonstrated the necessity of using “observers” to improve the performance of Feed-Forward Networks in such complex systems. The robustness of the forecasting capabilities of the “Observer Feed-Forward Networks” versus the distribution of the observers, including equidistant and random, and the motion of them, including stationary and moving was also investigated. We conclude that the method has broader applicability in dynamical system context when partial dynamical information about the system is available.