Learning Stochastic Behaviour of Aggregate Data

Learning nonlinear dynamics from aggregate datais a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not beobserved at the next time point, or the identity ofindividual is unavailable. This is in sharp contrastto 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. Insuch a sample based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving FPE. More importantly, our model can also readily handle high dimensional cases by leveraging deep neural networks. We demonstrate our approach in the context of aseries of synthetic and real-world data sets.