Numerical linear algebra in data assimilation
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Publication:6068266
DOI10.1002/gamm.202000014arXiv1912.13336OpenAlexW3086869348MaRDI QIDQ6068266
Publication date: 15 December 2023
Published in: GAMM-Mitteilungen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.13336
optimizationpreconditioningKalman filterGMRESsparse linear systemsconjugate gradientsKrylov methodsvariational data assimilationBayesian inverse problemsmodel order reductionlow-rank methods4D-Var3D-Var
Mathematical programming (90Cxx) Numerical linear algebra (65Fxx) Probabilistic methods, stochastic differential equations (65Cxx)
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Cites Work
- An optimization framework to improve 4D-Var data assimilation system performance
- POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation
- A reduced adjoint approach to variational data assimilation
- State estimation using model order reduction for unstable systems
- Regularization techniques for ill-posed inverse problems in data assimilation
- Conditioning and preconditioning of the variational data assimilation problem
- Solving ill-posed image processing problems using data assimilation
- Unbiased ensemble square root filters
- Large-scale Kalman filtering using the limited memory BFGS method
- Data assimilation in weather forecasting: a case study in PDE-constrained optimization
- Tidal flow forecasting using reduced rank square root filters
- Stable iterations for the matrix square root
- A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients
- Variational data assimilation with epidemic models
- Efficient methods for computing observation impact in 4D-Var data assimilation
- A low-rank approach to the solution of weak constraint variational data assimilation problems
- Dynamic data-driven reduced-order models
- Hessian-based covariance approximations in variational data assimilation
- A data assimilation technique applied to a predator-prey model
- Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems
- A matrix theoretic derivation of the Kalman filter
- Optimal reduced space for variational data assimilation
- A Bayesian tutorial for data assimilation
- Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter
- A time-parallel approach to strong-constraint four-dimensional variational data assimilation
- Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction
- Forecasting with imperfect models, dynamically constrained inverse problems, and gradient descent algorithms
- Parameter identification in explicit structural dynamics: performance of the extended Kalman filter
- Stochastic processes and filtering theory
- A Multilevel Approach for Computing the Limited-Memory Hessian and its Inverse in Variational Data Assimilation
- Inverse problems: A Bayesian perspective
- Likelihood-informed dimension reduction for nonlinear inverse problems
- Data-driven model reduction for the Bayesian solution of inverse problems
- Numerical Simulations with Data Assimilation Using an Adaptive POD Procedure
- Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
- Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems
- Levenberg--Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation
- Error Estimate for the Ensemble Kalman Filter Analysis Step
- Efficiency of a POD-based reduced second-order adjoint model in 4D-Var data assimilation
- Numerical solution of saddle point problems
- A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition
- Optimal Low-rank Approximations of Bayesian Linear Inverse Problems
- Hessian-based model reduction for large-scale systems with initial-condition inputs
- Principal component analysis in linear systems: Controllability, observability, and model reduction
- Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization
- Nonstationary inverse problems and state estimation
- Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
- Automatic Preconditioning by Limited Memory Quasi-Newton Updating
- The conditioning of least‐squares problems in variational data assimilation
- Data-Driven Computational Methods
- Some Relations Between Extended and Unscented Kalman Filters
- Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
- Model Reduction and Approximation
- Efficient generalized Golub–Kahan based methods for dynamic inverse problems
- Dynamic inverse problems: modelling—regularization—numerics
- Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS
- Linear and Nonlinear Inverse Problems with Practical Applications
- Approximate iterative methods for variational data assimilation
- Very large inverse problems in atmosphere and ocean modelling
- Computational Methods for Inverse Problems
- Lanczos Algorithms for Large Symmetric Eigenvalue Computations
- A Fresh Look at the Kalman Filter
- Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example
- AN ENSEMBLE KALMAN FILTER USING THE CONJUGATE GRADIENT SAMPLER
- Probabilistic Forecasting and Bayesian Data Assimilation
- Hessian‐based model reduction: large‐scale inversion and prediction
- Data Assimilation
- Robust Data Assimilation Using $L_1$ and Huber Norms
- Discrete Inverse Problems
- On Analysis Error Covariances in Variational Data Assimilation
- Data Assimilation
- Tomographic Imaging of Dynamic Objects With the Ensemble Kalman Filter
- Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse Problems
- The ensemble Kalman filter for combined state and parameter estimation
- Krylov space approximate Kalman filtering
- Ensemble filter techniques for intermittent data assimilation - a survey
- Introduction to Bayesian Scientific Computing
- Approximate Gauss–Newton Methods for Nonlinear Least Squares Problems
- Data assimilation: Mathematical and statistical perspectives
- Approximate Gauss–Newton methods for optimal state estimation using reduced‐order models
- A Reduced-Order Kalman Filter for Data Assimilation in Physical Oceanography
- Methods of conjugate gradients for solving linear systems
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