Ensemble generative filtering for sequential data assimilation in dynamical systems

2026-09-12

AI Summary

为解决数据同化中非高斯先验与计算效率的矛盾，提出集合生成滤波器(EnGF)，利用生成模型从适度大小的集合中抽取大量样本，提高过滤精度。

Abstract

Sequential data assimilation (DA) faces a fundamental trade-off: particle filters capture non-Gaussian cycling priors but require prohibitively large ensembles, whereas the ensemble Kalman filter (EnKF) is computationally efficient but constrained by its Gaussian assumption. As machine learning enables rapid model forecasts, exploiting non-Gaussian prior features via moderately large ensembles has become increasingly viable. To exploit this opportunity, we propose the ensemble generative filter (EnGF), a simple yet effective method for non-Gaussian filtering. The key idea is to fit a generative model to the forecast ensemble at each DA cycle and harness its defining strength, inexpensive sampling, to draw a much larger particle population for Bayesian analysis without any additional model forecasts; we adopt a Gaussian mixture model as a lightweight instance that can be fit cheaply from a moderate ensemble. To address practical challenges, we further extend the EnGF by introducing (i) a tempered EnGF using likelihood tempering to prevent particle degeneracy under informative observations and (ii) a latent EnGF that performs prior modeling and Bayesian updates in a reduced latent space for high-dimensional systems. Across chaotic systems (doubling map, Lorenz-63, and Lorenz-96) and a challenging shock-tube problem, the EnGF delivers clear and often substantial improvements over the EnKF, in some cases even approaching the filtering accuracy of a massive-ensemble particle filter at a small fraction of its cost.

Problem

• sequential data assimilation
• non-Gaussian priors
• ensemble Kalman filter
• computational efficiency

Innovation

• ensemble generative filter
• Gaussian mixture model
• likelihood tempering
• latent space