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We study the tipping point collective dynamics of an adaptivesusceptible-infected-susceptible (SIS) epidemiological network in adata-driven, machine learning-assisted manner. We identify aparameter-dependent effective stochastic differential equation (eSDE) in termsof physically meaningful coarse mean-field variables through a deep-learningResNet architecture inspired by numerical stochastic integrators. We constructan approximate effective bifurcation diagram based on the identified drift termof the eSDE and contrast it with the mean-field SIS model bifurcation diagram.We observe a subcritical Hopf bifurcation in the evolving network's effectiveSIS dynamics, that causes the tipping point behavior; this takes the form oflarge amplitude collective oscillations that spontaneously -- yet rarely --arise from the neighborhood of a (noisy) stationary state. We study thestatistics of these rare events both through repeated brute force simulationsand by using established mathematical/computational tools exploiting theright-hand-side of the identified SDE. We demonstrate that such a collectiveSDE can also be identified (and the rare events computations also performed) interms of data-driven coarse observables, obtained here via manifold learningtechniques, in particular Diffusion Maps. The workflow of our study isstraightforwardly applicable to other complex dynamics problems exhibitingtipping point dynamics.

Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling