Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a detailed description of these filters, with illustrative examples, together with new, more general, methods for solving the algebraic equations and with a new algorithm for parameter identification.
Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, the ensemble Kalman filter also has limitations due to its inherent Gaussian and linearity assumptions. These limitations can manifest themselves in dynamically inconsistent state estimates. We investigate this issue in this paper for highly oscillatory Hamiltonian systems with a dynamical behavior which satisfies …
Random-Feature Kalman Filtering for Linear PDE Data Assimilation
Ceyear Technologies Co., Ltd（中国电子科技集团公司第五十四研究所）；School of Mathematics and Statistics, Xidian University（西安电子科技大学数学与统计学院）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws
Division of Applied Mathematics, Linköping University（林雪平大学应用数学系）；Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）
We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier-Stokes equations of fluid dynamics, are characterized by a high sensitivity of solutions to perturbations of the initial data, a lack of rigorous global well-posedness results as well as possible non-convergence of numerical approximations. Under very mild and readily verifiable general hypotheses on the forward solution operator of such PDEs, we prove that the posterior measure expressing the solution of the Ba…
Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the applications, where the prediction of meteorological data are corrected given the observations. Numerous approaches are contained in data assimilation. One specific sequential method is the Kalman Filter. The core is to estimate unknown information with the new data that is measured and the prior data that is predicted. As a matter of fact, there are different impr…
Homotopy approaches to Bayesian inference have found widespread use especially if the Kullback-Leibler divergence between the prior and the posterior distribution is large. Here we extend one of these homotopy approach to include an underlying stochastic diffusion process. The underlying mathematical problem is closely related to the Schrödinger bridge problem for given marginal distributions. We demonstrate that the proposed homotopy approach provides a computationally tractable approximation to the underlying bridge problem. In particular, our implementation builds upon the widely used ensem…
Comparing an Ensemble Kalman Filter to a 4DVAR Data Assimilation System in Chaotic Dynamics
Universidade Federal de Pelotas – Faculdade de Meteorologia（佩洛塔斯联邦大学气象学院）；Departamento de Ciência e Tecnologia Aeroespacial – Instituto de Aeronáutica e Espaço – Divisão de Ciências Atmosféricas（航空航天科学与技术系 – 航空与航天研究所 – 大气科学部）
RWTH Aachen University（亚琛工业大学）；Technische Universität Braunschweig（布伦瑞克工业大学）；KAUST（阿卜杜拉国王科技大学）
This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in the literature. The updated mean of the CMF matches that of the posterior, obtained by applying Bayes' rule on the filter's forecast distribution. Moreover, we show that the CMF's updated covariance coincides with the expected conditional covariance. Implementing the EnCMF requires computing the conditional mean (CM). A likelihood-based estimator is prone to significant errors for small ensemble sizes, causing the f…
In this paper we introduce an agent-based model together with a particle filter approach for studying the spread of COVID-19. Investigations are performed on the metropolis of Tokyo, but other cities, regions or countries could have been equally chosen. A novel method for evaluating the effective reproduction number is one of the main outcome of our approach. Other unknown parameters and unknown populations are also evaluated. Uncertain quantities, as for example the ratio of symptomatic / asymptomatic agents, are tested and discussed, and the stability of our computations is examined. Detaile…
A Bayesian Approach to Multivariate Adaptive Localization in Ensemble-Based Data Assimilation with Time-Dependent Extensions
Virginia Polytechnic Institute and State University（弗吉尼亚理工大学）；Computational Science Laboratory, Department of Computer Science, Virginia Tech（弗吉尼亚理工学院计算机科学与计算科学实验室）
