跨多空间动力学联合建模的同步最佳传输。

IF 2.1 4区 数学 Q1 MATHEMATICS, APPLIED
SIAM Journal on Applied Mathematics Pub Date : 2025-01-01 Epub Date: 2025-02-11 DOI:10.1137/24m1667555
Zixuan Cang, Yanxiang Zhao
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引用次数: 0

摘要

最优传输已经成为从复杂数据中重建动力学的重要工具。随着可用的多面数据越来越多,系统通常可以跨多个空间进行表征。因此,在这些不同的空间中保持动态的一致性至关重要。为了应对这一挑战,我们引入了同步最优运输(SyncOT),这是一种新颖的方法,可以通过多个空间共同建模代表同一系统的动力学。给定空间之间的对应关系,SyncOT将所有考虑的空间中引起的动态的总成本最小化。用交错网格将该问题离散为有限维凸问题。然后提出了基于原始对偶算法的方法来解决离散化问题。各种数值实验证明了SyncOT的功能和特性,并验证了所提出算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
SYNCHRONIZED OPTIMAL TRANSPORT FOR JOINT MODELING OF DYNAMICS ACROSS MULTIPLE SPACES.

Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce synchronized optimal transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. Given the correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.

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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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