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Volume 38, Issue 3
A Network Based Approach for Unbalanced Optimal Transport on Surfaces

Jiangong Pan, Wei Wan, Yuejin Zhang, Chenlong Bao & Zuoqiang Shi

DOI: 10.4208/cicp.OA-2024-0173

Commun. Comput. Phys., 38 (2025), pp. 661-683.

Published online: 2025-08

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  • Abstract

In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to apply due to the difficulty of mesh generating. Neural network is easy to implement even for complicate geometry. Moreover, instead of solving the original dynamic formulation, we consider the Hamiltonian flow approach, i.e. Karush-Kuhn-Tucker system. Based on this approach, we can exploit mathematical structure of the optimal transport to construct the neural network and the loss function can be simplified. Extensive numerical experiments are conducted for surfaces with different geometry. We also test the method for point cloud with noise, which shows stability of this method. This method is also easy to generalize to diverse range of problems.

  • Keywords

Unbalanced optimal transport, Hamiltonian flow, point cloud, neural network.

  • AMS Subject Headings

65K10, 68T05, 68T07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-38-661, author = {Pan , JiangongWan , WeiZhang , YuejinBao , Chenlong and Shi , Zuoqiang}, title = {A Network Based Approach for Unbalanced Optimal Transport on Surfaces}, journal = {Communications in Computational Physics}, year = {2025}, volume = {38}, number = {3}, pages = {661--683}, abstract = {

In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to apply due to the difficulty of mesh generating. Neural network is easy to implement even for complicate geometry. Moreover, instead of solving the original dynamic formulation, we consider the Hamiltonian flow approach, i.e. Karush-Kuhn-Tucker system. Based on this approach, we can exploit mathematical structure of the optimal transport to construct the neural network and the loss function can be simplified. Extensive numerical experiments are conducted for surfaces with different geometry. We also test the method for point cloud with noise, which shows stability of this method. This method is also easy to generalize to diverse range of problems.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0173}, url = {http://global-sci.org/intro/article_detail/cicp/24311.html} }
TY - JOUR T1 - A Network Based Approach for Unbalanced Optimal Transport on Surfaces AU - Pan , Jiangong AU - Wan , Wei AU - Zhang , Yuejin AU - Bao , Chenlong AU - Shi , Zuoqiang JO - Communications in Computational Physics VL - 3 SP - 661 EP - 683 PY - 2025 DA - 2025/08 SN - 38 DO - http://doi.org/10.4208/cicp.OA-2024-0173 UR - https://global-sci.org/intro/article_detail/cicp/24311.html KW - Unbalanced optimal transport, Hamiltonian flow, point cloud, neural network. AB -

In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to apply due to the difficulty of mesh generating. Neural network is easy to implement even for complicate geometry. Moreover, instead of solving the original dynamic formulation, we consider the Hamiltonian flow approach, i.e. Karush-Kuhn-Tucker system. Based on this approach, we can exploit mathematical structure of the optimal transport to construct the neural network and the loss function can be simplified. Extensive numerical experiments are conducted for surfaces with different geometry. We also test the method for point cloud with noise, which shows stability of this method. This method is also easy to generalize to diverse range of problems.

Pan , JiangongWan , WeiZhang , YuejinBao , Chenlong and Shi , Zuoqiang. (2025). A Network Based Approach for Unbalanced Optimal Transport on Surfaces. Communications in Computational Physics. 38 (3). 661-683. doi:10.4208/cicp.OA-2024-0173
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