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Machine learning-based conditional mean filter: A generalization of the ensemble Kalman filter for nonlinear data assimilation: Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation

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Názov: Machine learning-based conditional mean filter: A generalization of the ensemble Kalman filter for nonlinear data assimilation: Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation
Autori: Hoang, Truong-Vinh, Krumscheid, Sebastian, Matthies, Hermann G., Tempone, Raúl
Prispievatelia: Applied Mathematics and Computational Science Program, Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Department of Mathematics, RWTH Aachen University, Gebäude-1953, 1.OG, Pontdriesch 14-16 52062 Aachen, Germany, Steinbuch Center for Computing and Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany, Technische Universität Braunschweig, Universitätsplatz 2, 38106 Braunschweig, Germany, Alexander von Humboldt professor in Mathematics of Uncertainty Quantification, RWTH Aachen University, Germany
Zdroj: Foundations of Data Science. 5:56-80
Publication Status: Preprint
Informácie o vydavateľovi: American Institute of Mathematical Sciences (AIMS), 2023.
Rok vydania: 2023
Predmety: ddc:004, FOS: Computer and information sciences, Computer Science - Machine Learning, Learning and adaptive systems in artificial intelligence, Machine Learning (stat.ML), 62M45, 62M20, 65C20, 86-08, Statistics - Computation, 01 natural sciences, Inference from stochastic processes and prediction, Machine Learning (cs.LG), Statistics - Machine Learning, conditional expectation, FOS: Mathematics, Mathematics - Numerical Analysis, Computation (stat.CO), 0105 earth and related environmental sciences, DATA processing & computer science, weather forecast, deep learning, Monte Carlo methods, Numerical Analysis (math.NA), Filtering in stochastic control theory, Neural nets and related approaches to inference from stochastic processes, nonlinear filter, inverse problem
Popis: 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 filter divergence. We develop a systematical methodology for integrating machine learning into the EnCMF based on the CM's orthogonal projection property. First, we use a combination of an artificial neural network (ANN) and a linear function, obtained based on the ensemble Kalman filter (EnKF), to approximate the CM, enabling the ML-EnCMF to inherit EnKF's advantages. Secondly, we apply a suitable variance reduction technique to reduce statistical errors when estimating loss function. Lastly, we propose a model selection procedure for element-wisely selecting the applied filter, i.e., either the EnKF or ML-EnCMF, at each updating step. We demonstrate the ML-EnCMF performance using the Lorenz-63 and Lorenz-96 systems and show that the ML-EnCMF outperforms the EnKF and the likelihood-based EnCMF.
Druh dokumentu: Article
Popis súboru: application/xml; application/pdf
ISSN: 2639-8001
DOI: 10.3934/fods.2022016
DOI: 10.48550/arxiv.2106.07908
Prístupová URL adresa: http://arxiv.org/abs/2106.07908
Rights: CC BY NC SA
Prístupové číslo: edsair.doi.dedup.....3ee17f9f58b53e1729cadc5dd3cc31e2
Databáza: OpenAIRE
Popis
Abstrakt: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 filter divergence. We develop a systematical methodology for integrating machine learning into the EnCMF based on the CM's orthogonal projection property. First, we use a combination of an artificial neural network (ANN) and a linear function, obtained based on the ensemble Kalman filter (EnKF), to approximate the CM, enabling the ML-EnCMF to inherit EnKF's advantages. Secondly, we apply a suitable variance reduction technique to reduce statistical errors when estimating loss function. Lastly, we propose a model selection procedure for element-wisely selecting the applied filter, i.e., either the EnKF or ML-EnCMF, at each updating step. We demonstrate the ML-EnCMF performance using the Lorenz-63 and Lorenz-96 systems and show that the ML-EnCMF outperforms the EnKF and the likelihood-based EnCMF.
ISSN:26398001
DOI:10.3934/fods.2022016