Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling

• URL: http://arxiv.org/abs/2602.17089v1
• Date: Thu, 19 Feb 2026 05:24:00 GMT
• Title: Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling
• Authors: Xinghao Dong, Huchen Yang, Jin-long Wu,
• Abstract summary: We show that flow matching in a lower-dimensional latent space is suited for fast sampling of closure models.<n>We control the latent space distortion and thus ensure the physical fidelity of the sampled closure term.
• Score: 1.665466637453776
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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