Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems

The behavior of large networked systems with underlying complex nonlinear dynamic are hard to predict. With increasing number of states, the problem becomes even harder. Quantifying uncertainty in such systems by conventional methods requires high computational time and the accuracy obtained in estimating the state variables can also be low. This paper presents a novel computational Uncertainty Quantifying (UQ) method for complex networked systems. Our approach is to represent the complex systems as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. First, we apply Non-negative Matrix Factorization (NMF) based decomposition method to partition the domain of the dynamical system into clusters, such that the inter-cluster interaction is minimized and the intra-cluster interaction is maximized. The decomposition method takes into account the dynamics of individual nodes to perform system decomposition. Initial validation results on two well-known dynamical systems have been performed. The validation results show that uncertainty propagation error quantified by RMS errors obtained through our algorithms are competitive or often better, compared to existing methods.