Parameterizations for ensemble Kalman inversion

Chada, Neil K.; Iglesias, Marco A.; Roininen, Lassi; Stuart, Andrew M.

doi:10.1088/1361-6420/aab6d9

Cited by 64 publications

(80 citation statements)

References 52 publications

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“…Using the analysis tools being developed in the work in progress [6] could be helpful in this context. • It would of interest to see how the techniques discussed in [5], where hierarchical EKI is introduced, could be improved by use of TEKI. The analysis presented here could be extended to the hierarchical setting.…”

Section: Casementioning

confidence: 99%

Tikhonov Regularization within Ensemble Kalman Inversion

Chada¹,

Stuart²,

Tong³

2020

SIAM J. Numer. Anal.

132

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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 basic form it regularizes ill-posed inverse problems through the subspace property: the solution found is in the linear span of the initial ensemble employed. In this work we demonstrate how further regularization can be imposed, incorporating prior information about the underlying unknown.In particular we study how to impose Tikhonov-like Sobolev penalties. As well as introducing this modified ensemble Kalman inversion methodology, we also study its continuous-time limit, proving ensemble collapse; in the language of multi-agent optimization this may be viewed as reaching consensus. We also conduct a suite of numerical experiments to highlight the benefits of Tikhonov regularization in the ensemble inversion context.

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Section: Casementioning

confidence: 99%

Tikhonov Regularization within Ensemble Kalman Inversion

Chada¹,

Stuart²,

Tong³

2020

SIAM J. Numer. Anal.

132

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“…An alternative to TV regularization of level sets is specification of a Gaussian random field prior for the auxiliary field used to generate the level set (e.g. Chada et al 2018). Using a Gaussian random field prior allows explicit control of the dominant length scale and roughness of the resultant level set, as shown in Fig.…”

Section: The Level Set Methodsmentioning

confidence: 99%

Geometric and level set tomography using ensemble Kalman inversion

Muir

Tsai

2019

Geophysical Journal International

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Summary Tomography is one of the cornerstones of geophysics, enabling detailed spatial descriptions of otherwise invisible processes. However, due to the fundamental ill-posedness of tomography problems, the choice of parametrizations and regularizations for inversion significantly affect the result. Parametrizations for geophysical tomography typically reflect the mathematical structure of the inverse problem. We propose, instead, to parametrize the tomographic inverse problem using a geologically motivated approach. We build a model from explicit geological units that reflect the a priori knowledge of the problem. To solve the resulting large-scale nonlinear inverse problem, we employ the efficient Ensemble Kalman Inversion scheme, a highly parallelizable, iteratively regularizing optimizer that uses the ensemble Kalman filter to perform a derivative-free approximation of the general iteratively-regularized Levenberg-Marquardt method. The combination of a model specification framework that explicitly encodes geological structure and a robust, derivative-free optimizer enables the solution of complex inverse problems involving non-differentiable forward solvers and significant a priori knowledge. We illustrate the model specification framework using synthetic and real data examples of near-surface seismic tomography using the factored eikonal fast marching method as a forward solver for first arrival travel times. The geometrical and level set framework allows us to describe geophysical hypotheses in concrete terms, and then optimize and test these hypotheses, helping us to answer targeted geophysical questions.

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“…We then compare the proposed technique against monomial based SMC as well as an ensemble Kalman inversion (EKI) technique that arises naturally from the adaptive SMC setting. This EKI methodology has been proposed in [14] as an alternative of [15]. Here this approach is modified to incorporate a mutation with the invariant measure.…”

Section: Contribution Of This Workmentioning

confidence: 99%

Transform-based particle filtering for elliptic Bayesian inverse problems

Ruchi¹,

Dubinkina²,

Iglesias³

2019

Inverse Problems

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We introduce optimal transport based resampling in adaptive SMC. We consider elliptic inverse problems of inferring hydraulic conductivity from pressure measurements. We consider two parametrizations of hydraulic conductivity: by Gaussian random field, and by a set of scalar (non-)Gaussian distributed parameters and Gaussian random fields. We show that for scalar parameters optimal transport based SMC performs comparably to monomial based SMC but for Gaussian highdimensional random fields optimal transport based SMC outperforms monomial based SMC. When comparing to ensemble Kalman inversion with mutation (EKI), we observe that for Gaussian random fields, optimal transport based SMC gives comparable or worse performance than EKI depending on the complexity of the parametrization. For non-Gaussian distributed parameters optimal transport based SMC outperforms EKI.

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Parameterizations for ensemble Kalman inversion

Cited by 64 publications

References 52 publications

Tikhonov Regularization within Ensemble Kalman Inversion

Tikhonov Regularization within Ensemble Kalman Inversion

Geometric and level set tomography using ensemble Kalman inversion

Transform-based particle filtering for elliptic Bayesian inverse problems

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