Related papers: A network based approach for unbalanced optimal tr…

In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…

In this paper, we solve unbalanced optimal transport (UOT) problem on surfaces represented by point clouds. Based on alternating direction method of multipliers algorithm, the original UOT problem can be solved by an iteration consists of…

In this work, we propose a novel method for generating 3D point clouds that leverage properties of hyper networks. Contrary to the existing methods that learn only the representation of a 3D object, our approach simultaneously finds a…

To account for the randomness of propagation channels and interference levels in hierarchical spectrum sharing, a novel approach to multihop routing is introduced for cognitive random access networks, whereby packets are randomly routed…

We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification,…

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…

Point cloud registration plays a crucial role in various fields, including robotics, computer graphics, and medical imaging. This process involves determining spatial relationships between different sets of points, typically within a 3D…

A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the…

We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…

Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…

The design of fluid channel structures of reactors or separators of chemical processes is key to enhancing the mass transfer processes inside the devices. However, the systematic design of channel topological structures is difficult for…

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…

We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear…

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…

Unpaired point cloud completion is crucial for real-world applications, where ground-truth data for complete point clouds are often unavailable. By learning a completion map from unpaired incomplete and complete point cloud data, this task…

Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…

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 novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…

Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to…

The challenge of dynamic traffic demand in mobile networks is tackled by moving cells based on unmanned aerial vehicles. Considering the tremendous potential of unmanned aerial vehicles in the future, we propose a new heuristic algorithm…