A Variational Surface-Evolution Approach to Optimal Transport over Transitioning Compact Supports with Domain Constraints

IF 17.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-16 DOI:10.3390/fluids9050118

Anthony Yezzi

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.

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在有域约束条件的过渡紧凑支承上实现最佳传输的变式面进化方法

我们研究了 Rn 中具有过渡紧凑支撑的密度之间的最佳质量传输问题，方法是考虑时空中连续插值支撑边界 Γ 的几何形状，质量密度在该边界内根据贝纳模和布雷尼尔的流体动力学框架演化。我们用 Rn+1=R×Rn 中的点、矢量和集合来处理这种时空嵌入的几何形状，并将质量密度和速度融合为一个紧凑集合 ω⊂Rn+1 上的时空螺线管矢量场 W|Ω→Rn+1。然后，我们利用时空曲面 Γ 的形状梯度勾勒出支持边界 ∂Ω，对 W 及其支持进行联合优化。这很容易适应时空限制，包括障碍物或必须访问的区域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.