Flow Matching for Efficient and Scalable Data Assimilation

TL;DR

The paper introduces the ensemble flow filter (EnFF), a flow matching-based framework that enhances data assimilation efficiency and scalability in high-dimensional systems without training, outperforming existing methods in cost-accuracy tradeoffs.

Contribution

EnFF is a novel, training-free flow matching framework that generalizes classical filters and improves data assimilation in high-dimensional nonlinear systems.

Findings

EnFF achieves better cost-accuracy tradeoffs in high-dimensional benchmarks.

EnFF is scalable and flexible for various data assimilation tasks.

The method generalizes classical filters like the bootstrap particle filter and ensemble Kalman filter.

Abstract

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 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.