Despite the recent popularity of neural network-based solvers for optimal transport (OT),
there is no standard quantitative way to evaluate their performance. In this paper, we …

Monge map refers to the optimal transport map between two probability distributions and
provides a principled approach to transform one distribution to another. In spite of the rapid …

The dynamical formulation of the optimal transport can be extended through various choices
of the underlying geometry ($\textit {kinetic energy} $), and the regularization of density …

Reconstructing dynamics using samples from sparsely time-resolved snapshots is an
important problem in both natural sciences and machine learning. Here, we introduce a new …

We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-
agent systems. We formulate the problem as one of steering the collective towards a target …

We propose a novel mean field games (MFGs) based GAN (generative adversarial network)
framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a …

We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-
agent systems. We formulate the problem as one of steering the collective towards a target …