标题： 潜在-EnSF：一种用于稀疏观测数据高维数据同化的潜在集合评分滤波器 显示英文标题

标题： Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data

摘要： 复杂物理系统的精确建模和预测通常依赖于数据同化技术来修正模型模拟中存在的误差。传统的集合卡尔曼滤波（EnKF）及其变种以及最近开发的集合评分滤波器（EnSF），在处理高维非线性贝叶斯滤波问题时面临显著挑战，特别是在稀疏观测条件下，而这在实际应用中非常普遍。 本文提出了一种新颖的数据同化方法——潜在变量集合评分滤波器（Latent-EnSF），该方法利用EnSF结合全状态和稀疏观测的高效且一致的潜在表示，以应对非线性贝叶斯滤波中状态高维性和观测高稀疏性的联合挑战。我们引入了一个耦合的变分自编码器（VAE），它具有两个编码器，能够以一种由潜在分布匹配和正则化以及一致的状态重构保证的方式对全状态和稀疏观测进行编码。通过与几种方法的比较，我们在浅水波传播和中程天气预报这两个具有复杂模型的应用中展示了Latent-EnSF对于高度空间和时间稀疏观测更高的准确性、更快的收敛速度和更高的效率。 显示英文摘要

摘要： Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as the recently developed Ensemble Score Filters (EnSF) face significant challenges when dealing with high-dimensional and nonlinear Bayesian filtering problems with sparse observations, which are ubiquitous in real-world applications. In this paper, we propose a novel data assimilation method, Latent-EnSF, which leverages EnSF with efficient and consistent latent representations of the full states and sparse observations to address the joint challenges of high dimensionlity in states and high sparsity in observations for nonlinear Bayesian filtering. We introduce a coupled Variational Autoencoder (VAE) with two encoders to encode the full states and sparse observations in a consistent way guaranteed by a latent distribution matching and regularization as well as a consistent state reconstruction. With comparison to several methods, we demonstrate the higher accuracy, faster convergence, and higher efficiency of Latent-EnSF for two challenging applications with complex models in shallow water wave propagation and medium-range weather forecasting, for highly sparse observations in both space and time.