Temporal Normalizing Flows

Analyzing and interpreting time-dependent stochastic data requires accurate and robust density estimation. In this paper we extend the concept of normalizing flows to so-called temporal Normalizing Flows (tNFs) to estimate time dependent distributions, leveraging the full spatio-temporal information present in the dataset. Our approach is unsupervised, does not require an a-priori characteristic scale and can accurately estimate multi-scale distributions of vastly different length scales. We illustrate tNFs on sparse datasets of Brownian and chemotactic walkers, showing that the inclusion of temporal information enhances density estimation. Finally, we speculate how tNFs can be applied to fit and discover the continuous PDE underlying a stochastic process.