  We present a machine learning (ML)-assisted framework bridging manifold
learning, neural networks, Gaussian processes, and Equation-Free multiscale
modeling, for (a) detecting tipping points in the emergent behavior of complex
systems, and (b) characterizing probabilities of rare events (here,
catastrophic shifts) near them. Our illustrative example is an event-driven,
stochastic agent-based model (ABM) describing the mimetic behavior of traders
in a simple financial market. Given high-dimensional spatiotemporal data --
generated by the stochastic ABM -- we construct reduced-order models for the
emergent dynamics at different scales: (a) mesoscopic Integro-Partial
Differential Equations (IPDEs); and (b) mean-field-type Stochastic Differential
Equations (SDEs) embedded in a low-dimensional latent space, targeted to the
neighborhood of the tipping point. We contrast the uses of the different models
and the effort involved in learning them.
