Network reconstruction may not mean dynamics prediction

Abstract

With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate, financial, ecological, and neural systems. The underlying mechanisms are commonly encoded into network structures, e.g., capturing how constituents interact with each other to produce emergent behavior. Here, we address whether a good network reconstruction suggests a good dynamics prediction. The answer is quite dependent on the nature of the supplied (observed) dynamics sequences measured on the complex system. When the dynamics are not chaotic, network reconstruction implies dynamics prediction. In contrast, even if a network can be well reconstructed from the chaotic time series (chaos means that many unstable dynamics states coexist), the prediction of the future dynamics can become impossible as at some future point the prediction error will be amplified. This is explained by using dynamical mean-field theory on a toy model of random recurrent neural networks.