We propose a machine learning framework based on Flow Matching (FM) to identify critical properties in many-body systems efficiently. Using the 2D XY model as a benchmark, we demonstrate that a single network, trained only on configurations from a small ($32\times 32$) lattice at sparse temperature points, effectively generalizes across both temperature and system size. This dual generalization enables two primary applications for large-scale computational physics: (i) a rapid "train-small, predict-large" strategy to locate phase transition points for significantly larger systems ($128\times 128$) without retraining, facilitating efficient finite-size scaling analysis; and (ii) the fast generation of high-fidelity, decorrelated initial spin configurations for large-scale Monte Carlo simulations, providing a robust starting point that bypasses the long thermalization times of traditional samplers. These capabilities arise from the combination of the Flow Matching framework, which learns stable probability-flow vector fields, and the inductive biases of the U-Net architecture that capture scale-invariant local correlations. Our approach offers a scalable and efficient tool for exploring the thermodynamic limit, serving as both a rapid explorer for phase boundaries and a high-performance initializer for high-precision studies.

翻译：我们提出了一种基于流匹配（FM）的机器学习框架，用于高效识别多体系统的临界特性。以二维XY模型为基准，我们证明：仅使用小型（$32\times 32$）晶格在稀疏温度点上的构型进行训练的单一网络，能够有效泛化至不同温度与系统尺寸。这种双重泛化能力为大规模计算物理研究带来两项主要应用：（i）通过“小规模训练、大规模预测”的快速策略，无需重新训练即可定位更大系统（$128\times 128$）的相变点，从而支持高效的有限尺寸标度分析；（ii）为大规模蒙特卡洛模拟快速生成高保真、去关联的初始自旋构型，提供能够规避传统采样器长热化时间的稳健初始点。这些能力源于流匹配框架（学习稳定的概率流向量场）与U-Net架构（捕捉尺度不变的局部关联性）归纳偏置的结合。我们的方法为探索热力学极限提供了可扩展且高效的工具，既可作为相边界的快速探索器，也能作为高精度研究的高性能初始化器。