Transform-based particle filtering for elliptic Bayesian inverse problems

Ruchi, Sangeetika; Dubinkina, Svetlana; Iglesias, Marco A.

doi:10.1088/1361-6420/ab30f3

Cited by 11 publications

(16 citation statements)

References 27 publications

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“…According to the theory in [27], α n must be carefully selected, together with the stopping criteria, in order to ensure the stability of the LM scheme. The approach for selecting α n in the LM proposed in [27] has been adapted to the EKI framework in [2,16], and subsequently used in [3,12,14,[28][29][30]. As we discuss in the next section, this approach relies on tuning parameters that, unless carefully chosen, can lead to unnecessary large number of iterations n * .…”

Section: The Inverse Problem Framework With Ensemble Kalman Inversionmentioning

confidence: 99%

“…where we have made the standard assumption that y = G(u) + η with η ∼ N(0, Γ). Modern computational approaches [28,[32][33][34][35] for high-dimensional Bayesian inverse problems use the tempering approach that consists of introducing N intermediate measures {μ t n } N n=1 between the prior and the posterior. These measures are defined by…”

Section: Eki As a Gaussian Approximation In The Bayesian Tempering Sementioning

confidence: 99%

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Adaptive regularisation for ensemble Kalman inversion

Iglesias

Yang

2021

Inverse Problems

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We propose a new regularisation strategy for the classical ensemble Kalman inversion (EKI) framework. The strategy consists of: (i) an adaptive choice for the regularisation parameter in the update formula in EKI, and (ii) criteria for the early stopping of the scheme. In contrast to existing approaches, our parameter choice does not rely on additional tuning parameters which often have severe effects on the efficiency of EKI. We motivate our approach using the interpretation of EKI as a Gaussian approximation in the Bayesian tempering setting for inverse problems. We show that our parameter choice controls the symmetrised Kullback-Leibler divergence between consecutive tempering measures. We further motivate our choice using a heuristic statistical discrepancy principle. We test our framework using electrical impedance tomography with the complete electrode model. Parameterisations of the unknown conductivity are employed which enable us to characterise both smooth or a discontinuous (piecewise-constant) fields. We show numerically that the proposed regularisation of EKI can produce efficient, robust and accurate estimates, even for the discontinuous case which tends to require larger ensembles and more iterations to converge. We compare the proposed technique with a standard method of choice and demonstrate that the proposed method is a viable choice to address computational efficiency of EKI in practical/operational settings.

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Section: The Inverse Problem Framework With Ensemble Kalman Inversionmentioning

confidence: 99%

Section: Eki As a Gaussian Approximation In The Bayesian Tempering Sementioning

confidence: 99%

Adaptive regularisation for ensemble Kalman inversion

Iglesias

Yang

2021

Inverse Problems

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“…1 a and b and as it has been reported in the literature, e.g. [28,29]. When uncertainty is in both permeability and boundary conditions, we investigate methods performance for two numerical setups.…”

Section: Data Assimilation Without Localizationmentioning

confidence: 93%

“…We have shown that though localization makes the ensemble transform particle filter deteriorates a posterior estimation of the leading modes, it makes the method applicable to highdimensional problems. In [29], instead of localization, we have implemented tempering to the ensemble transform particle filter (TETPF). We have shown that iterations based on temperatures [21,23] handle notably strongly nonlinear cases and that TETPF is able to predict multimodal distributions for high-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

“…This groundwater model was first used as benchmark for inverse modelling in [11]. It has been used as a test model for the identification of parameters, for example with iterative regularization methods [20], an ensemble Kalman approach [4], and in our previous work with particle filtering [28,29]. In this paper in addition to uncertain log permeability defined as a Gaussian process, we assume an error in boundary conditions that is non-Gaussian distributed.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of regularized ensemble Kalman filter and tempered ensemble transform particle filter for an elliptic inverse problem with uncertain boundary conditions

Dubinkina

Ruchi

2019

Comput Geosci

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In this paper, we focus on parameter estimation for an elliptic inverse problem. We consider a 2D steady-state singlephase Darcy flow model, where permeability and boundary conditions are uncertain. Permeability is parameterized by the Karhunen-Loeve expansion and thus assumed to be Gaussian distributed. We employ two ensemble-based data assimilation methods: ensemble Kalman filter and ensemble transform particle filter. The formal one approximates mean and variance of a Gaussian probability function by means of an ensemble. The latter one transforms ensemble members to approximate any posterior probability function. Ensemble Kalman filter considered here is employed with regularization and localization-R(L)EnKF. Ensemble transform particle filter is also employed with a form of regularization called tempering and localization-T(L)ETPF. Regularization is required for highly non-linear problems, where prior is updated to posterior via a sequence of intermediate probability measures. Localization is required for small ensemble sizes to remove spurious correlations. We have shown that REnKF outperforms TETPF. We have shown that localization improves estimations of both REnKF and TETPF. In numerical experiments when uncertainty is only in permeability, TLETPF outperforms RLEnKF. When uncertainty is both in permeability and in boundary conditions, TLETPF outperforms RLEnKF only for a large ensemble size 1000. Furthermore, when uncertainty is both in permeability and in boundary conditions but we do not account for error in boundary conditions in data assimilation, RLEnKF outperforms TLETPF.

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