用低维隐空间流匹配加速随机闭包建模，采样快100倍且保持物理准确性
Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling
- 在低维隐空间做流匹配，实现单步采样替代迭代扩散
- 相比传统方法采样速度提升达两个数量级，最快可达100倍
- 通过隐空间正则化保留系统拓扑结构，少量数据即可学习有效闭包模型
近年来发展的扩散模型虽能生成高质量且多样化的样本，适合学习随机闭包模型，但采样速度慢是其主要短板。本文通过2D柯尔莫戈罗夫流动的数值实验系统比较基于传输的生成模型，发现低维隐空间中的流匹配方法可实现单步采样，比迭代扩散方法快达两个数量级。为控制隐空间失真以保障采样项的物理保真度，对比了联合训练带来的隐式正则化与两种显式正则化：保度量（MP）和几何感知（GA）约束。无论显式或隐式正则化，所学隐空间均继承原始复杂动力系统低维流形的关键拓扑信息，使无需大量训练数据即可学习有效的随机闭包模型。
原文摘要 · Abstract (English)
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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