Laplacian graph based approach for uncertainty quantification of large scale dynamical systems

Design of nonlinear dynamic complex systems that are robust to uncertainties requires usage of uncertainty quantification methods. With a large number of states, quantifying uncertainty by conventional methods is computationally prohibitive. Conventional methods are also prone to error. When the number of interacting variables is large, it is prudent, if not imperative, to take advantage of special structural features of a decomposed system and come up with a substantial reduction in dimensionality to get a solution for analyzing the whole system. In this paper, we propose two new methods of state space decomposition of large-scale dynamical systems. The proposed methods not only take into consideration the initial values of the state variables but also the evolution of the trajectories of the states with time. The efficacy of the novel state space partitioning schemes on selected uncertainty quantification test problems are outlined. Initial results show that our state partitioning schemes are competitive or often better, compared to existing methods.