A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909581692633088 |
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| author | Zhang, Tan Wang, Zhongjian Xin, Jack Zhang, Zhiwen |
| author_facet | Zhang, Tan Wang, Zhongjian Xin, Jack Zhang, Zhiwen |
| contents | This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions under varying physical parameters. Solutions are approximated as empirical measures of particles that adaptively align with the high-gradient regions. The core idea of the BDP method is to learn both forward and reverse mappings (between the uniform and a non-trivial target distribution) by minimizing the discrete 2-Wasserstein distance (W2) and optimizing the transition map therein by a minibatch technique. We present numerical results demonstrating the effectiveness of the BDP method for learning and generating solutions to Keller-Segel chemotaxis systems in the presence of laminar flows and Kolmogorov flows with chaotic streamlines in three space dimensions. The BDP outperforms two recent representative single-step flow matching and diffusion models (rectified flow and shortcut diffusion models) in the generative AI literature. However when the target distribution is high-dimensional (4 and above), e.g. a mixture of two Gaussians, the single-step diffusion models scale better in dimensions than BDP in terms of W2-accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11851 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems Zhang, Tan Wang, Zhongjian Xin, Jack Zhang, Zhiwen Computational Physics This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions under varying physical parameters. Solutions are approximated as empirical measures of particles that adaptively align with the high-gradient regions. The core idea of the BDP method is to learn both forward and reverse mappings (between the uniform and a non-trivial target distribution) by minimizing the discrete 2-Wasserstein distance (W2) and optimizing the transition map therein by a minibatch technique. We present numerical results demonstrating the effectiveness of the BDP method for learning and generating solutions to Keller-Segel chemotaxis systems in the presence of laminar flows and Kolmogorov flows with chaotic streamlines in three space dimensions. The BDP outperforms two recent representative single-step flow matching and diffusion models (rectified flow and shortcut diffusion models) in the generative AI literature. However when the target distribution is high-dimensional (4 and above), e.g. a mixture of two Gaussians, the single-step diffusion models scale better in dimensions than BDP in terms of W2-accuracy. |
| title | A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2504.11851 |