  Learning nonlinear dynamics from aggregate data is a challenging problem
because the full trajectory of each individual is not available, namely, the
individual observed at one time may not be observed at the next time point, or
the identity of individual is unavailable. This is in sharp contrast to
learning dynamics with full trajectory data, on which the majority of existing
methods are based. We propose a novel method using the weak form of Fokker
Planck Equation (FPE) -- a partial differential equation -- to describe the
density evolution of data in a sampled form, which is then combined with
Wasserstein generative adversarial network (WGAN) in the training process. In
such a sample-based framework we are able to learn the nonlinear dynamics from
aggregate data without explicitly solving the partial differential equation
(PDE) FPE. We demonstrate our approach in the context of a series of synthetic
and real-world data sets.
