  Deriving closed-form, analytical expressions for reduced-order models, and
judiciously choosing the closures leading to them, has long been the strategy
of choice for studying phase- and noise-induced transitions for agent-based
models (ABMs). In this paper, we propose a data-driven framework that pinpoints
phase transitions for an ABM in its mean-field limit, using a smaller number of
variables than traditional closed-form models. To this end, we use the manifold
learning algorithm Diffusion Maps to identify a parsimonious set of data-driven
latent variables, and show that they are in one-to-one correspondence with the
expected theoretical order parameter of the ABM. We then utilize a deep
learning framework to obtain a conformal reparametrization of the data-driven
coordinates that facilitates, in our example, the identification of a single
parameter-dependent ODE in these coordinates. We identify this ODE through a
residual neural network inspired by a numerical integration scheme (forward
Euler). We then use the identified ODE -- enabled through an odd symmetry
transformation -- to construct the bifurcation diagram exhibiting the phase
transition.

Dynamical Systems;Machine Learning;Multiagent Systems