Comparison of Linearization and Graph Clustering Methods for Uncertainty Quantification of Large Scale Dynamical Systems


Mukjerjee, A., Rai, R., Singla, P., Singh, T., and Patra, A.


International Journal of Uncertainty Quantification, 7(1).


The behavior of large nonlinear dynamic systems underlying complex networked systems is hard to predict. Uncertainty quantification (UQ) 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 method focused on performing effective uncertainty quantification in large networked systems comprising weakly coupled subsystems (WCSs). Our approach to model complex systems is to represent them as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. We present time-domain and space-domain linearization techniques and outline a framework that integrates the concept of linearization with graph clustering algorithm to identify WCSs in high-dimensional complex networks. The outlined technique enables identification of WCSs and thus facilitates effective UQ. The work presented in this paper also highlights the review and analytic comparison of a couple of clustering techniques [spectral clustering (SC) and non-negative matrix factorization (NMF)] that are applicable in the domain of UQ of large scale dynamical systems. The SC and NMF based clustering methods have been applied to study the UQ of scalable coupled oscillators. A new metric has been developed to compare the performance of the clustering algorithms in the UQ domain. Also, key factors that affect the performance of the algorithms have been identified. We also present the results of the statistical analysis to identify the key factors contributing to the performance of the clustering based system decomposition framework.

   Author = {A. Mukherjee, R. Rai, P. Singla, T. Singh and A. Patra},
   Journal = {International Journal for Uncertainty Quantification},
   Month = {June},
   Title = {Comparison of Linearization and Graph Clustering Methods for Uncertainty Quantification of Large Scale Dynamical Systems},
   Volume = {7},
   Number = {1},
   Year = {2017}