Related papers: Numerical simulation of optimal transport paths
A path-planning algorithm for connected and non-connected automated road vehicles on multilane motorways is derived from the opportune formulation of an optimal control problem. In this framework, the objective function to be minimized…
Simulation is a valuable tool for traffic management experts to assist them in refining and improving transportation systems and anticipating the impact of possible changes in the infrastructure network before their actual implementation.…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
This paper serves as a user's guide to sampling strategies for sliced optimal transport. We provide reminders and additional regularity results on the Sliced Wasserstein distance. We detail the construction methods, generation time…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
This paper proposes an approach to perform travel demand calibration for high-resolution stochastic traffic simulators. It employs abundant travel times at the path-level, departing from the standard practice of resorting to scarce…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals $N$ and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible…
This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
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 introduces the first statistically consistent estimator of the optimal transport map between two probability distributions, based on neural networks. Building on theoretical and practical advances in the field of Lipschitz neural…
Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the…
We link the theory of optimal transportation to the theory of integer partitions. Let $\mathscr P(n)$ denote the set of integer partitions of $n \in \mathbb N$ and write partitions $\pi \in \mathscr P(n)$ as $(n_1, \dots, n_{k(\pi)})$.…
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…
We study a tensor optimal transport (TOT) problem for $d\ge 2$ discrete measures. This is a linear programming problem on $d$-tensors. We introduces an interior point method (ipm) for $d$-TOT with a corresponding barrier function. Using a…