递归流匹配提升科学模拟速度与精度，实现高效实时仿真。
Recursive Flow Matching
- 通过递归自洽机制对齐多尺度轨迹，降低离散化误差。
- 相比基线流匹配，均方误差降低超15%，2-4步预测精度领先。
- 在复杂科学任务中实现比扩散模型快20倍的推理速度。
生成模型已成为求解物理系统和建模复杂时空动态的强大范式。然而，如何在不增加计算成本的前提下实现高物理精度仍是核心挑战，现有方法普遍存在速度与保真度之间的权衡。本文提出递归流匹配（RecFM），一种用于预测复杂时空动态的生成框架。RecFM通过强制多尺度轨迹自洽性，有效减少离散化误差，在多个物理任务指标上表现更优。据我们所知，这是首个在科学系统中实现高保真度一至几步（2-4步）动态生成的方法，性能可媲美先进的多步求解器。在多个具有挑战性的科学基准测试中，RecFM相较领先的基于扩散模型的模拟器提速最高达20倍，同时提升预测精度；相较于原始流匹配，均方误差降低超过15%，为实时科学模拟提供了可扩展、高效的解决方案。
原文摘要 · Abstract (English)
Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20$\times$ speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.
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