Flow Matching for Efficient and Scalable Data Assimilation
This work addresses the problem of efficient and scalable state estimation for dynamical systems, particularly in high-dimensional settings, representing an incremental advancement over existing generative models like the ensemble score filter.
The paper tackles the computational expense of data assimilation in high-dimensional nonlinear systems by introducing the ensemble flow filter (EnFF), a training-free framework based on flow matching that accelerates sampling and generalizes classical filters, achieving improved cost-accuracy tradeoffs and scalability in experiments.
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.