An ensemble score filter for tracking high-dimensional nonlinear dynamical systems

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-10-22 DOI:10.1016/j.cma.2024.117447
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Abstract

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF addresses this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterize the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation method that uses a mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial–temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems while also saving a tremendous amount of time spent on training neural networks. High-dimensional Lorenz-96 systems are used to demonstrate the performance of our method. EnSF provides superior performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter, in reliably and efficiently tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimensions) with highly nonlinear observation processes.
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用于跟踪高维非线性动力系统的集合得分过滤器
我们提出了一种集合得分滤波器(EnSF),用于解决高维非线性滤波问题,且精度极高。现有滤波方法(如粒子滤波器或集合卡尔曼滤波器)的一个主要缺点是处理高维和高度非线性问题的精度较低。EnSF 利用在伪时域中定义的基于分数的扩散模型来描述滤波密度的演变,从而解决了这一难题。EnSF 将递归更新滤波密度函数的信息存储在分数函数中,而不是存储在一组有限蒙特卡罗样本中(粒子滤波器和集合卡尔曼滤波器中使用)。与现有的通过训练神经网络来逼近得分函数的扩散模型不同,我们开发了一种无需训练的得分估计方法,该方法使用基于迷你批处理的蒙特卡罗估计器直接逼近任意伪空间-时间位置的得分函数,在解决高维非线性问题时提供了足够的精度,同时还节省了大量训练神经网络的时间。我们使用高维 Lorenz-96 系统来证明我们方法的性能。与最先进的局部集合变换卡尔曼滤波器相比,EnSF 在可靠、高效地跟踪具有高度非线性观测过程的极高维 Lorenz 系统(多达 1,000,000 维)方面表现出色。
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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