Wasserstein distances are metrics on probability distributions inspired by the problem of
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …

Transport-based techniques for signal and data analysis have recently received increased
interest. Given their ability to provide accurate generative models for signal intensities and …

Optimal transport maps between two probability distributions $\mu $ and $\nu $ on $\R^ d $
have found extensive applications in both machine learning and statistics. In practice, these …

Optimal transport distances, otherwise known as Wasserstein distances, have recently
drawn ample attention in computer vision and machine learning as powerful discrepancy …

In this article we survey r-adaptive (or moving grid) methods for solving time-dependent
partial differential equations (PDEs). Although these methods have received much less …

We propose a novel end-to-end non-minimax algorithm for training optimal transport
mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex …

We propose and analyze a nonparametric region-based active contour model for
segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel …

Frechet means and Procrustes analysis in Wasserstein space Page 1 Bernoulli 25(2), 2019,
932–976 https://doi.org/10.3150/17-BEJ1009 Fréchet means and Procrustes analysis in …

We study the use of amortized optimization to predict optimal transport (OT) maps from the
input measures, which we call Meta OT. This helps repeatedly solve similar OT problems …

Soft sensors suffer from high manufacturing tolerances and signal drift from long‐term
usage, which degrades their practicality. Although deep learning has recently been …