Temporal Normalizing Flows
This provides a method for analyzing time-dependent stochastic data, which is incremental as it builds on existing normalizing flows by incorporating temporal information.
The authors tackled the problem of estimating time-dependent distributions from stochastic data by extending normalizing flows to temporal Normalizing Flows (tNFs), which leverage spatio-temporal information to accurately estimate multi-scale distributions, as demonstrated on sparse datasets of Brownian and chemotactic walkers.
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.