A Network Based Approach for Unbalanced Optimal Transport on Surfaces (Communications in Computational Physics, 2025)
In this paper, we present a neural network approach to address the dynamicunbalanced optimal transport problem on surfaces with point cloud representation.For surfaces with point cloud representation, traditional method is difficult to applydue to the difficulty of mesh generating. Neural network is easy to implement evenfor 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. Extensivenumerical experiments are conducted for surfaces with different geometry. We alsotest the method for point cloud with noise, which shows stability of this method. Thismethod is also easy to generalize to diverse range of problems.
Keywords: Unbalanced optimal transport; Hamiltonian flow; point cloud; neural network.