Flow Mesh: A Velocity-Regularized Flow Matching Framework for Stable Distributional Modeling of Physical Fields on Unstructured Meshes

arXiv:2610.33204v1 Announce Type: new Abstract: Thermal-fluid field distributions underpin the analysis and operation of energy infrastructure, from nuclear-reactor cooling channels to industrial heat exchangers, but resolving these distributions through computational fluid dynamics requires prohibitively large simulation ensembles. Their complex geometries also demand unstructured meshes that are poorly accommodated by generative models developed for regular grids. Here we introduce FlowMesh, a generative framework that combines permutation-invariant mesh encoding with deterministic latent flow matching and an l1 penalty on the learned transport velocity. FlowMesh generates full-field realizations directly on fixed unstructured meshes without auxiliary grid interpolation or a stochastic denoising chain. Across lid-driven-cavity, pressurized-water-reactor subchannel and heat-exchanger datasets, evaluated over six matched training seeds, FlowMesh achieves macro-averaged probability-density-function coverage of 91.7%-97.0%, exceeding an architecture-controlled latent diffusion model by $11.6$--$45.4$ percentage points. Latent-velocity regularization increases coverage by $3.8$ percentage points for reactor flows and 1.1 points for heat-exchanger flows, while reducing temperature-field Kullback--Leibler divergence by 1.7-2.4-fold. Each full-field realization requires 1.23 \pm 0.15 s, providing a 585--1902-fold wall-clock acceleration over computational fluid dynamics. FlowMesh therefore makes large-scale generative characterization of thermal-fluid states computationally feasible, providing a foundation for data-driven analysis and digital-twin development in fixed-geometry energy systems.