DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min optimization during training and does not impose any restriction on the network structure. Theoretically we establish a weak convergence guarantee and a quantitative error bound between the learned map and the optimal transport map. Our numerical experiments validate the theoretical results and the effectiveness of the new approach, particularly on real-world tasks.

@article{li2025_2506.23429,
  title={ DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee },
  author={ Yingyuan Li and Aokun Wang and Zhongjian Wang },
  journal={arXiv preprint arXiv:2506.23429},
  year={ 2025 }
}