Related papers: Numerical simulation of optimal transport paths
We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule…
We propose a new algorithm to approximate the Earth Mover's distance (EMD). Our main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar $L_1$ type minimization. We use a regularization which…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
In this paper a search algorithm is proposed to find a sub optimal path for a non-holonomic system. For this purpose the algorithm starts sampling the front part of the vehicle and moves towards the destination with a cost function. The…
We investigate the fast transport of an atom or a packet of atoms by different kinds of non-harmonic traps including power-law traps. The study is based on the reverse engineering method. Exact results are obtained and applied to design…
We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction…
Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…
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,…
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering techniqe based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
In a random ray method of neutral particle transport simulation, each iteration begins by sampling a set of rays before proceeding to solve the characteristic transport equation along the linear paths the rays follow. Historically,…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
Traffic simulations are made more realistic by giving individual drivers intentions, i.e. an idea of where they want to go. One possible implementation of this idea is to give each driver an exact pre-computed path, that is, a sequence of…
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…
Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…
Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…
The costs incurred in a mobile robot (MR) change due to change in physical and environmental factors. Usually, there are two approaches to consider these costs, either explicitly modelling these different factors to calculate the cost or…