Uncertainty Quantification of Multi-Scale Resilience in Nonlinear Complex Networks using Arbitrary Polynomial Chaos

In an increasing connected world, resilience is an important ability for a system to retain its original function when perturbations happen. Even though we understand small-scale resilience well, our understanding of large-scale networked resilience is limited. Recent research in network-level resilience and node-level resilience pattern has advanced our understanding of the relationship between topology and dynamics across network scales. However, the effect of uncertainty in a large-scale networked system is not clear, especially when uncertainties cascade between connected nodes. In order to quantify resilience uncertainty across the network resolutions (macro to micro), we develop an arbitrary polynomial chaos (aPC) expansion method to estimate the resilience subject to parameter uncertainties with arbitrary distributions. For the first time and of particular importance, is our ability to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk. We test this using a generic networked bi-stable system and this will aid practitioners to both understand macro-scale behaviour and make micro-scale interventions.