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Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
We study the theoretical convergence of the nonlinear least-squares splitting method for the Monge-Amp\`ere equation in which each iteration decouples the pointwise nonlinearity from the differential operator and consists of a local…
Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning"…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
We give a necessary and sufficient condition on the cost function so that the map solution of Monge's optimal transportation problem is continuous for arbitrary smooth positive data. This condition was first introduced by Ma, Trudinger and…
This work proposes a novel, general and robust method of determining bond micromoduli for anisotropic linear elastic bond-based peridynamics. The problem of finding a discrete distribution of bond micromoduli that reproduces an anisotropic…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
Integration against, and hence sampling from, high-dimensional probability distributions is of essential importance in many application areas and has been an active research area for decades. One approach that has drawn increasing attention…
(Abridged) We study the properties of anisotropic and axisymmetric velocity ellipsoids from maps of the gas velocity dispersion in nearby galaxies. This data allow us to measure the azimuthal-to-radial axis ratio of gas velocity ellipsoids,…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
A numerical method for the solution of the elliptic Monge-Ampere Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is presented. A local representation of the OT boundary…
In parallel with advances in microscale imaging techniques, the fields of biology and materials science have focused on precisely extracting particle properties based on their diffusion behavior. Although the majority of real-world…
Using first-principles calculations, we elucidate microscopic mechanisms of perpendicular magnetic anisotropy (PMA)in Fe/MgO magnetic tunnel junctions through evaluation of orbital and layer resolved contributions into the total anisotropy…
The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics. In particular, the rank energy (RE) and…
Transport coefficients associated with the mass flux of a binary mixture of Maxwell molecules under uniform shear flow are exactly determined from the Boltzmann kinetic equation. A normal solution is obtained via a Chapman--Enskog-like…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
Defect transport is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant…