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

Complex systems derive sophisticated behavioural dynamics by connecting individual component dynamics via a complex network. The resilience of complex systems is a critical ability to regain desirable behaviour after perturbations. In the past years our understanding of large-scale networked resilience is largely confined to proprietary agent-based simulations or topological analysis of graphs. However, we know dynamics and topology matter equally and the impact of model uncertainty of the system remains unsolved especially on individual node. In order to quantify resilience uncertainty across the network resolutions (from macro-scale network statistics to individual node dynamics), we propose an arbitrary polynomial chaos (aPC) expansion method to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk on a single node. We test this using both a generic networked bi-stable system and also established ecological and work force commuter network dynamics to demonstrate applicability. This framework will aid practitioners to both understand macro-scale behaviour and make micro-scale interventions