发表机构
Scripps Institution of Oceanography, University of California San Diego; Computing + Mathematical Sciences, California Institute of Technology; Center for Computational Mathematics, Flatiron Institute（斯克里普斯海洋学研究所，加州大学圣地亚哥分校; 计算与数学科学系，加州理工学院; 计算数学中心，平流层研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对序贯数据同化中粒子滤波成本高与EnKF高斯假设局限的权衡，提出系综生成式滤波器（EnGF），通过生成模型廉价采样扩充粒子群体，在混沌系统和激波管问题上显著优于EnKF，接近大规模粒子滤波精度。
AI 中文摘要
序贯数据同化（DA）面临一个基本权衡：粒子滤波器能够捕捉非高斯循环先验，但需要极其庞大的系综；而系综卡尔曼滤波器（EnKF）计算高效，却受限于其高斯假设。随着机器学习使得模型预报快速化，利用中等规模系综来挖掘非高斯先验特征已变得越来越可行。为利用这一机遇，我们提出了系综生成式滤波器（EnGF），一种简单而有效的非高斯滤波方法。其关键思想是在每个同化周期对预报系综拟合一个生成模型，并利用其定义性优势——廉价采样——来抽取远大于原系综的粒子群体以进行贝叶斯分析，而无需额外的模型预报；我们采用高斯混合模型作为轻量级实例，可从中等规模系综中廉价拟合。为应对实际挑战，我们进一步扩展了EnGF，引入了（i）使用似然退火的退火EnGF，以防止在信息量大的观测下出现粒子退化，以及（ii）潜在EnGF，在高维系统中于降维潜在空间内进行先验建模和贝叶斯更新。在混沌系统（倍频映射、Lorenz-63和Lorenz-96）以及一个具有挑战性的激波管问题中，EnGF相比EnKF带来了清晰且通常显著的改进，在某些情况下甚至以极小成本接近大规模系综粒子滤波器的滤波精度。
英文摘要
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.
