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Related papers: Iterated Kalman Methodology For Inverse Problems

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The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…

Numerical Analysis · Mathematics 2019-03-20 Michael Herty , Giuseppe Visconti

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

Optimization and Control · Mathematics 2019-10-11 Jiacheng Wu , Jian-Xun Wang , Shawn C. Shadden

In this study, we consider an ensemble Kalman inversion (EKI) for the numerical solution of time-fractional diffusion inverse problems (TFDIPs). Computational challenges in the EKI arise from the need for repeated evaluations of the forward…

Numerical Analysis · Mathematics 2019-02-26 Fenglian Yang , Liang Yan

We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…

Numerical Analysis · Mathematics 2020-09-15 Philipp A. Guth , Claudia Schillings , Simon Weissmann

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

Dynamical Systems · Mathematics 2025-11-07 Diego Olguín , Axel Osses , Héctor Ramírez

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…

Numerical Analysis · Mathematics 2024-12-20 Neil K. Chada , Andrew M. Stuart , Xin T. Tong

Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…

Computational Physics · Physics 2020-06-24 Xin-Lei Zhang , Carlos Michelén-Ströfer , Heng Xiao

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…

Optimization and Control · Mathematics 2016-01-20 Marco A. Iglesias

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the…

Optimization and Control · Mathematics 2023-08-15 Himali Singh , Arpan Chattopadhyay , Kumar Vijay Mishra

Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we…

Atmospheric and Oceanic Physics · Physics 2026-05-19 Pavel Perezhogin , Alistair Adcroft , Laure Zanna

Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…

Dynamical Systems · Mathematics 2019-10-17 Alfredo Garbuno-Inigo , Franca Hoffmann , Wuchen Li , Andrew M. Stuart

Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…

Computation · Statistics 2019-10-23 Guillermo Scheffler , Juan Ruiz , Manuel Pulido

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random…

Machine Learning · Computer Science 2025-02-26 Oliver R. A. Dunbar , Nicholas H. Nelsen , Maya Mutic

Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…

Machine Learning · Statistics 2024-01-04 Jonathan Schmidt , Philipp Hennig , Jörg Nick , Filip Tronarp

In this paper, the ensemble consider Kalman filter is proposed to mitigate the negative effects of uncertain parameters in nonlinear dynamic and measurement models. The ensemble Kalman filter can avoid using the Jacobian matrices and reduce…

Systems and Control · Electrical Eng. & Systems 2019-06-18 Tai-shan Lou , Nan-hua Chen , Hua Xiong , Ya-xi Li , Lei Wang

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…

Numerical Analysis · Mathematics 2026-01-21 Aryeh Keating , Mirjeta Pasha

Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…

Numerical Analysis · Mathematics 2020-10-13 Zhaoxing Li , Jiguang Sun , Liwei Xu

The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to…

Numerical Analysis · Mathematics 2022-01-25 Oliver R. A. Dunbar , Andrew B. Duncan , Andrew M. Stuart , Marie-Therese Wolfram

Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of…

Optimization and Control · Mathematics 2018-10-11 Wei Kang , Liang Xu

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…

Applications · Statistics 2021-03-12 Elizabeth Hou , Earl Lawrence , Alfred O. Hero