We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In this case, we derive a simple formulation for the constrained dynamical OT.
@article{arxiv.1807.00937,
title = {Constrained dynamical optimal transport and its Lagrangian formulation},
author = {Wuchen Li and Stanley Osher},
journal= {arXiv preprint arXiv:1807.00937},
year = {2018}
}