{"title":"A Variational Surface-Evolution Approach to Optimal Transport over Transitioning Compact Supports with Domain Constraints","authors":"Anthony Yezzi","doi":"10.3390/fluids9050118","DOIUrl":null,"url":null,"abstract":"We examine the optimal mass transport problem in Rn between densities with transitioning compact support by considering the geometry of a continuous interpolating support boundary Γ in space-time within which the mass density evolves according to the fluid dynamical framework of Benamou and Brenier. We treat the geometry of this space-time embedding in terms of points, vectors, and sets in Rn+1=R×Rn and blend the mass density and velocity as well into a space-time solenoidal vector field W|Ω→Rn+1 over a compact set Ω⊂Rn+1. We then formulate a joint optimization for W and its support using the shaped gradient of the space-time surface Γ outlining the support boundary ∂Ω. This easily accommodates spatiotemporal constraints, including obstacles or mandatory regions to visit.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":"5 1","pages":""},"PeriodicalIF":16.4000,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/fluids9050118","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We examine the optimal mass transport problem in Rn between densities with transitioning compact support by considering the geometry of a continuous interpolating support boundary Γ in space-time within which the mass density evolves according to the fluid dynamical framework of Benamou and Brenier. We treat the geometry of this space-time embedding in terms of points, vectors, and sets in Rn+1=R×Rn and blend the mass density and velocity as well into a space-time solenoidal vector field W|Ω→Rn+1 over a compact set Ω⊂Rn+1. We then formulate a joint optimization for W and its support using the shaped gradient of the space-time surface Γ outlining the support boundary ∂Ω. This easily accommodates spatiotemporal constraints, including obstacles or mandatory regions to visit.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.