相关论文: Optimal micropatterns in 2D transport networks and…

We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…

We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…

The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…

In this work, we present a novel tool for reconstructing networks from corrupted images. The reconstructed network is the result of a minimization problem that has a misfit term with respect to the observed data, and a physics-based…

In recent work arXiv:2109.07820 we have shown the equivalence of the widely used nonconvex (generalized) branched transport problem with a shape optimization problem of a street or railroad network, known as (generalized) urban planning…

We consider two variational models for transport networks, an urban planning and a branched transport model, in both of which there is a preference for networks that collect and transport lots of mass together rather than transporting all…

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…

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…

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…

We analyse the following inverse problem. Given a nonconvex functional (from a specific, but quite general class) of normal, codimension-1 currents (which in two spatial dimensions can be interpreted as transportation networks), find the…

Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected…

We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…

This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…

One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem…

In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal…