用流匹配加速数据同化，提升高维非线性系统的效率与可扩展性
Flow Matching for Efficient and Scalable Data Assimilation
- 基于流匹配设计无训练采样框架，支持灵活的流结构设计
- 在高维基准测试中实现更低计算成本与更优精度平衡
- 适合需要高效、可扩展数据同化的气象、海洋等科学领域
数据同化（DA）旨在从噪声观测中估计动态系统状态。近年来，生成模型如集合评分滤波器（EnSF）在高维非线性场景中提升了DA性能，但计算开销大。本文提出无训练的集合流滤波器（EnFF），基于流匹配（FM）框架，加速采样并支持灵活的流设计。EnFF采用蒙特卡洛估计边际流场，局部引导实现观测同化，并引入新颖的流路径以利用贝叶斯数据同化公式。该方法泛化了经典滤波器，如粒子滤波器和集合卡尔曼滤波器。在多个高维基准测试中，EnFF展现出更优的成本-精度权衡与可扩展性，凸显流匹配在高效、可扩展数据同化中的潜力。代码已开源：https://github.com/Utah-Math-Data-Science/Data-Assimilation-Flow-Matching。
原文摘要 · Abstract (English)
Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationally expensive. We introduce the ensemble flow filter (EnFF), a training-free, flow matching (FM)-based framework that accelerates sampling and offers flexibility in flow design. EnFF uses Monte Carlo estimators for the marginal flow field, localized guidance for observation assimilation, and utilizes a novel flow path that exploits the Bayesian DA formulation. It generalizes classical filters such as the bootstrap particle filter and ensemble Kalman filter. Experiments on high-dimensional benchmarks demonstrate EnFF's improved cost-accuracy tradeoffs and scalability, highlighting FM's potential for efficient, scalable DA. Code is available at https://github.com/Utah-Math-Data-Science/Data-Assimilation-Flow-Matching.
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