Cyber-physical systems encompass multiple system domains (i.e., water, energy, networking) with heterogeneous goals and complexity of interactions. Existing technologies do not address the disparate time and spatial scales across the many system domains, especially with the latest threats and challenge spaces. New methods to manage resilience of systems, including integrating new computing and sensing strategies, machine learning and artificial intelligence, as well as advanced resilience analytics and prediction, are required to ensure that cyber-physical systems can withstand adverse events. This article summarizes the results of the December 2021 Society for Risk Analysis “Workshop on Resilience Analytics: Methodology and Applications to Cyber-Energy Systems” in which a multidisciplinary team of researchers, policymakers, military, and industry professionals met to identify priorities for research.

Resilience describes the capacity of systems to react to, withstand, adjust to, and recover from disruptive events. Despite numerous metrics proposed to quantify resilience, few studies predict these metrics or the restoration time to nominal performance levels, and these studies often focus on a single domain. This paper introduces three methods to model system performance and resilience metrics, which are applicable to various engineering and social science domains. These models utilize reliability engineering techniques, including bathtub-shaped functions, mixture distributions, and regression analysis incorporating event intensity covariates. Historical U.S. job loss data during recessions are used to evaluate these approaches’ predictive accuracy. This study computes goodness-of-fit measures, confidence intervals, and resilience metrics. The results show that bathtub-shaped functions and mixture distributions accurately predict curves possessing V, U, L, and J shapes but struggle with W and K shapes involving multiple disruptions or sudden performance drops. In contrast, covariate-based models effectively track all curve types, including complex W and K shapes, like the successive shocks in the 1980 U.S. recession and the sharp decline in the 2020 U.S. recession. These models achieve a high predictive accuracy for future performance and resilience metrics, evidenced by the low sum of square errors and high adjusted coefficients of determination.