This repository numerically studies the convergence rates for approximating transport maps in higher-dimensional function spaces using different metrics and divergences. We study the approximation of one-dimensional maps using the Wasserstein distance between push-forward measures and the Kullback-Leibler divergence between pull-back measures. The code for minimizing the KL divergence over a space of monotone maps relies on the toolbox developed as part of the ATM package that is available here. More details on the experiments and the theoretical analysis for these studies can be found in the accompanying preprint.
Ricardo Baptista (Caltech), Bamdad Hosseini (Washington), Nikola Kovachki (NVIDIA), Youssef Marzouk (MIT), Amir Sagiv (Columbia)
E-mails: rsb@caltech.edu, bamdadh@uw.edu, nkovachki@nvidia.com, ymarz@mit.edu, as6011@columbia.edu