We study nonparametric estimation of the interaction term in a McKean-Vlasov model where noisy observations are drawn from the nonlinear parabolic PDE arising in the mean-field limit as the number of interacting particles grows to infinity. In this model, the long-time invariant state can be uninformative about the interaction potential. We therefore show that under certain regularity conditions on the initial state, the short-time behaviour of this system already contains sufficient information to consistently recover the interaction potential using a Bayesian approach.

This is joint work with Richard Nickl and Greg Pavliotis.