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Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but…
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
Unprecedented control over the manufacture of electronic devices on nanometer scale has allowed to perform highly controllable and fine-tuned experiments in the quantum regime where exotic effects can nowadays be measured. In quantum dot…
Optimal experimental design (OED) plays an important role in the problem of identifying uncertainty with limited experimental data. In many applications, we seek to minimize the uncertainty of a predicted quantity of interest (QoI) based on…
Hard visual attention is a promising approach to reduce the computational burden of modern computer vision methodologies. Hard attention mechanisms are typically non-differentiable. They can be trained with reinforcement learning but the…
We introduce the transport-and-pack(TAP) problem, a frequently encountered instance of real-world packing, and develop a neural optimization solution based on reinforcement learning. Given an initial spatial configuration of boxes, we seek…
This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…
This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage…
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 address this issue for quadratic-cost transport --…
We present a registration method for model reduction of parametric partial differential equations with dominating advection effects and moving features. Registration refers to the use of a parameter-dependent mapping to make the set of…
Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting…
$\textbf{This is the conference version of our paper: Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner}$. Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale…
We study transport in topologically disordered networks that are subjected to an environment that induces classical diffusion. The dynamics is phenomenologically described within the framework of the recently introduced quantum stochastic…
We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this…
The problem of efficiently delivering data within networks is very important nowadays, especially in the context of the large volumes of data which are being produced each year and of the increased data access needs of the users. Efficient…
The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows.For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow's…