We study the tipping point collective dynamics of an adaptive
susceptible-infected-susceptible (SIS) epidemiological network in a
data-driven, machine learning-assisted manner. We identify a
parameter-dependent effective stochastic differential equation (eSDE) in terms
of physically meaningful coarse mean-field variables through a deep-learning
ResNet architecture inspired by numerical stochastic integrators. We construct
an approximate effective bifurcation diagram based on the identified drift term
of the eSDE and contrast it with the mean-field SIS model bifurcation diagram.
We observe a subcritical Hopf bifurcation in the evolving network's effective
SIS dynamics, that causes the tipping point behavior; this takes the form of
large amplitude collective oscillations that spontaneously -- yet rarely --
arise from the neighborhood of a (noisy) stationary state. We study the
statistics of these rare events both through repeated brute force simulations
and by using established mathematical/computational tools exploiting the
right-hand-side of the identified SDE. We demonstrate that such a collective
SDE can also be identified (and the rare events computations also performed) in
terms of data-driven coarse observables, obtained here via manifold learning
techniques, in particular Diffusion Maps. The workflow of our study is
straightforwardly applicable to other complex dynamics problems exhibiting
tipping point dynamics.Comment: 22 pages, 12 figure