Well posedness and convergence analysis of the ensemble Kalman inversion

DOI10.1088/1361-6420/ab149czbMath1432.62325arXiv1810.08463OpenAlexW2897923806WikidataQ128139827 ScholiaQ128139827MaRDI QIDQ5228017

Dirk Blömker, Simon Weissmann, Claudia Schillings, Philipp Wacker

Publication date: 8 August 2019

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.08463

zbMATH Keywords

optimizationBayesian inverse problemsensemble Kalman inversionwell-posedness and accuracy

Mathematics Subject Classification ID

Applications of statistics to environmental and related topics (62P12) Image analysis in multivariate analysis (62H35) Neural nets and related approaches to inference from stochastic processes (62M45)

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Uses Software

• EnKF

Cites Work

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• Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation
• A dynamical systems framework for intermittent data assimilation
• Iterative regularization for ensemble data assimilation in reservoir models
• On the stability and the uniform propagation of chaos properties of ensemble Kalman-Bucy filters
• Performance analysis of local ensemble Kalman filter
• Ensemble filter methods with perturbed observations applied to nonlinear problems
• A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
• Nonlinear stability and ergodicity of ensemble based Kalman filters
• Deterministic Mean-Field Ensemble Kalman Filtering
• Multilevel ensemble Kalman filtering
• Ensemble Kalman methods for inverse problems
• Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time
• Stochastic Differential Equations in Infinite Dimensions
• Long-Time Stability and Accuracy of the Ensemble Kalman--Bucy Filter for Fully Observed Processes and Small Measurement Noise
• Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit
• Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems
• A Strongly Convergent Numerical Scheme from Ensemble Kalman Inversion
• Bayesian inversion in resin transfer molding
• Convergence analysis of ensemble Kalman inversion: the linear, noisy case
• Performance of Ensemble Kalman Filters in Large Dimensions
• Analysis of the Ensemble Kalman Filter for Inverse Problems
• Tomographic Imaging of Dynamic Objects With the Ensemble Kalman Filter