Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917281582284800 |
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| author | Dong, Xinghao Yang, Huchen Wu, Jin-long |
| author_facet | Dong, Xinghao Yang, Huchen Wu, Jin-long |
| contents | Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models. Compared to other types of generative AI models, such as GANs and VAEs, the sampling speed is known as a key disadvantage of diffusion models. By systematically comparing transport-based generative models on a numerical example of 2D Kolmogorov flows, we show that flow matching in a lower-dimensional latent space is suited for fast sampling of stochastic closure models, enabling single-step sampling that is up to two orders of magnitude faster than iterative diffusion-based approaches. To control the latent space distortion and thus ensure the physical fidelity of the sampled closure term, we compare the implicit regularization offered by a joint training scheme against two explicit regularizers: metric-preserving (MP) and geometry-aware (GA) constraints. Besides offering a faster sampling speed, both explicitly and implicitly regularized latent spaces inherit the key topological information from the lower-dimensional manifold of the original complex dynamical system, which enables the learning of stochastic closure models without demanding a huge amount of training data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17089 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling Dong, Xinghao Yang, Huchen Wu, Jin-long Machine Learning Dynamical Systems Computational Physics Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models. Compared to other types of generative AI models, such as GANs and VAEs, the sampling speed is known as a key disadvantage of diffusion models. By systematically comparing transport-based generative models on a numerical example of 2D Kolmogorov flows, we show that flow matching in a lower-dimensional latent space is suited for fast sampling of stochastic closure models, enabling single-step sampling that is up to two orders of magnitude faster than iterative diffusion-based approaches. To control the latent space distortion and thus ensure the physical fidelity of the sampled closure term, we compare the implicit regularization offered by a joint training scheme against two explicit regularizers: metric-preserving (MP) and geometry-aware (GA) constraints. Besides offering a faster sampling speed, both explicitly and implicitly regularized latent spaces inherit the key topological information from the lower-dimensional manifold of the original complex dynamical system, which enables the learning of stochastic closure models without demanding a huge amount of training data. |
| title | Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling |
| topic | Machine Learning Dynamical Systems Computational Physics |
| url | https://arxiv.org/abs/2602.17089 |