In the aftermath of a natural disaster, knowledge of the connectivity of different regions of infrastructure networks is crucial to aid decision makers. For large-scale networks it can be extremely time-consuming to obtain a converged estimate by performing a large number of Monte Carlo simulations to compute the network failure probability. To reduce computational requirements, this work develops a surrogate model using an AdaBoost classifier for predicting probabilities of disconnections between node clusters in lifeline infrastructure networks. The proposed approach uses spectral clustering to partition the network, and it estimates the connectivity of these clusters using an AdaBoost classifier. Numerical experiments on a California gas distribution network demonstrate that using the surrogate model to determine cluster connectivity introduces less than five percent error and is two orders of magnitude faster than methods using an exact network model to estimate the probability of network failure through Monte Carlo simulations.