[2604.05700] Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space

Computer Science > Machine Learning arXiv:2604.05700 (cs) [Submitted on 7 Apr 2026] Title:Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space Authors:Li Kunpeng, Wan Chenguang, Qu Zhisong, Lim Kyungtak, Virginie Grandgirard, Xavier Garbet, Yu Hua, Ong Yew Soon View a PDF of the paper titled Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space, by Li Kunpeng and 7 other authors View PDF HTML (experimental) Abstract:High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as diffusion models and Flow Matching, have shown promising performance, they are fundamentally constrained by their discrete, pixel-based nature. This limitation restricts their applicability in turbulence computing, where data inherently exists in a functional form. To address this gap, we propose Functional Optimal Transport Conditional Flow Matching (FOT-CFM), a generative framework defined directly in infinite-dimensional function space. Unlike conventional approaches defined on fixed grids, FOT-CFM treats physical fields as elements of an infinite-dimensional Hilbert space, and learns resolution-invariant generative dynamics directly at the level of probability measures. By integrating Optimal Transport (OT) theory, we construct deterministi...