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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| Published in: | Journal of computational and applied mathematics Vol. 476; p. 117132 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.04.2026
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| ISSN: | 0377-0427 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 117132 |
| Author | Guo, Xu Li, Yiqun Zheng, Xiangcheng Bai, Songhai Zhu, Yan |
| Author_xml | – sequence: 1 givenname: Songhai surname: Bai fullname: Bai, Songhai email: 202315037@mail.sdu.edu.cn organization: Geotechnical and Structural Engineering Center, Shandong University, 250061, Jinan, Shandong, China – sequence: 2 givenname: Xu surname: Guo fullname: Guo, Xu email: guoxu@sdu.edu.cn organization: Geotechnical and Structural Engineering Center, Shandong University, 250061, Jinan, Shandong, China – sequence: 3 givenname: Yiqun surname: Li fullname: Li, Yiqun email: YiqunLi24@outlook.com organization: School of Mathematics and Statistics, Wuhan University, 430072, Wuhan, Hubei, China – sequence: 4 givenname: Xiangcheng surname: Zheng fullname: Zheng, Xiangcheng email: xzheng@sdu.edu.cn organization: School of Mathematics, Shandong University, 250100, Jinan, Shandong, China – sequence: 5 givenname: Yan surname: Zhu fullname: Zhu, Yan email: zhuyan0077@126.com organization: Geotechnical and Structural Engineering Center, Shandong University, 250061, Jinan, Shandong, China |
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| Keywords | Space–time fractional General-proximal primal–dual hybrid gradient algorithm 91A16 Anomalous transport 35Q89 35R11 Nonlocal dispersive optimal transport |
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