Georgia Institute of Technology College of Sciences

Zoom link: https://gatech.zoom.us/j/4561289292

Abstract: In recent years we have seen the popularity of optimal transport and deep learning. Optimal transport theory works well in studying differences among distributions, while deep learning is powerful to analyze high dimensional data. In this presentation we will discuss some of our recent work that combine both optimal transport and deep learning on data-driven problems. We will cover four parts in this presentation. The first part is studying stochastic behavior from aggregate data where we recover the drift term in an SDE, via the weak form of Fokker-Planck equation. The second part is applying Wasserstein distance on the optimal density control problem where we parametrize the control strategy by a neural network. In the third part we will show a novel form of computing Wasserstein distance, geometric and map all together in a scalable way. And in the final part, we consider an inverse OT problem where we recover cost function when an observed policy is given.