Related papers: Multiscale Strategies for Computing Optimal Transp…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
Machine learning (ML) techniques have recently enabled enormous gains in sensitivity to new phenomena across the sciences. In particle physics, much of this progress has relied on excellent simulations of a wide range of physical processes.…
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…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
This paper addresses the problem of finding multiple near-optimal, spatially-dissimilar paths that can be considered as alternatives in the decision making process, for finding optimal corridors in which to construct a new road. We further…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions…
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each…
Multi-task learning has gained popularity due to the advantages it provides with respect to resource usage and performance. Nonetheless, the joint optimization of parameters with respect to multiple tasks remains an active research topic.…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be…
Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
A multimodal network encodes relationships between the same set of nodes in multiple settings, and network alignment is a powerful tool for transferring information and insight between a pair of networks. We propose a method for multimodal…