A nonlocal dispersive optimal transport: Formulation and algorithm

We propose a unified framework that effectively characterizes challenging phenomena such as anomalous transport in heterogeneous media and long-range memory effects and interactions. This framework transports agent densities from a prescribed initial distribution to a terminal distribution while min...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 476; p. 117132
Main Authors: Bai, Songhai, Guo, Xu, Li, Yiqun, Zheng, Xiangcheng, Zhu, Yan
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2026
Subjects:
Anomalous transport
General-proximal primal–dual hybrid gradient algorithm
Nonlocal dispersive optimal transport
Space–time fractional
Space–time fractional
General-proximal primal–dual hybrid gradient algorithm
91A16
Anomalous transport
35Q89
35R11
Nonlocal dispersive optimal transport
ISSN:0377-0427
Online Access:Get full text
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Summary:We propose a unified framework that effectively characterizes challenging phenomena such as anomalous transport in heterogeneous media and long-range memory effects and interactions. This framework transports agent densities from a prescribed initial distribution to a terminal distribution while minimizing the associated energy cost. Motivated by optimal transport theory, we introduce a nonlocal dispersive optimal transport (NDOT) model governed by a space–time fractional partial differential equation (PDE). We solve the NDOT formulation using the general-proximal primal–dual hybrid gradient (G-prox PDHG) algorithm, and then introduce a novel preconditioner derived from the discretization of the space–time fractional PDE to accelerate the convergence. Numerical experiments – especially those with target states represented by power functions typical of fractional differential equation solutions – show that our model substantially reduces kinetic energy costs compared with its integer-order counterparts, highlighting its effectiveness and applicability for complex phenomena such as anomalous transport in heterogeneous environments.
ISSN:0377-0427
DOI:10.1016/j.cam.2025.117132