Related papers: 4DVAR by ensemble Kalman smoother
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
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…
An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem $\min \norm{Ax-b}_2$, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is…
Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear…
This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
We formulate approximate Bayesian inference in non-conjugate temporal and spatio-temporal Gaussian process models as a simple parameter update rule applied during Kalman smoothing. This viewpoint encompasses most inference schemes,…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
Stochastic gradient updates are widely used for their efficiency and scalability, but their effective step sizes can depend strongly on feature scaling and local model sensitivity. Gauss-Newton methods address such scale effects through…
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
We introduce a new multilevel ensemble Kalman filter method (MLEnKF) which consists of a hierarchy of independent samples of ensemble Kalman filters (EnKF). This new MLEnKF method is fundamentally different from the preexisting method…
In this paper, we introduce a Gauss-Newton method for solving the complex phase retrieval problem. In contrast to the real-valued setting, the Gauss-Newton matrix for complex-valued signals is rank-deficient and, thus, non-invertible. To…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is…
The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving…
In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advantage of both the least squares structure and the neural…