Parameter estimation for subsurface flow using ensemble data assimilation

Over the years, different data assimilation methods have been implemented to acquire improved estimations of model parameters by adjusting the uncertain parameter values in such a way that the mathematical model approximates the observed data as closely and consistently as possible. However, most of these methods are developed on the assumption of Gaussianity, e.g. Ensemble Kalman Filters, whic

Accounting for model error in Tempered Ensemble Transform Particle Filter and its application to non-additive model error

In this paper, we trivially extend Tempered (Localized) Ensemble Transform Particle Filter—T(L)ETPF—to account for model error. We examine T(L)ETPF performance for non-additive model error in a low-dimensional and a high-dimensional test problem. The former one is a nonlinear toy model, where uncertain parameters are non-Gaussian distributed but model error is Gaussian distributed. The latter one is

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

In this paper, we focus on parameter estimation for an elliptic inverse problem. We consider a 2D steady-state single- phase 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 transf

Transform-based particle filtering for elliptic Bayesian inverse problems

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 high- dimensional 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

Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation

Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte Carlo (SMC) method, whereby resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion, it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity, and the method is not as robust as ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy-inspired regularisation factor to the underlying optimal transport problem that allows the high computational cost to be considerably reduced via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as a hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov chain Monte Carlo methods results are computed as a benchmark

Data underlying the paper: Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

A dataset for the article "Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling" by S. Ruchi and S. Dubinkina in Nonlin. Processes Geophys. 2018 Accurate estimation of subsurface geological parameters, e.g. permeability, is essential for the oil industry. This is done by combining observations of pressure with a mathematical model using data assimilation. We show that computationally affordable ensemble transform data assimilation methods are suitable for the parameter estimation. For a small number of uncertain parameters, ensemble transform particle filter performs comparably to ensemble transform Kalman filter in terms of the mean estimation. For a large number of uncertain parameters, ensemble transform particle filter performs comparably to ensemble transform Kalman filter only when either localization or the leading modes are used

Data underlying the paper: Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

A dataset for the article "Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling" by S. Ruchi and S. Dubinkina in Nonlin. Processes Geophys. 2018 Accurate estimation of subsurface geological parameters, e.g. permeability, is essential for the oil industry. This is done by combining observations of pressure with a mathematical model using data assimilation. We show that computationally affordable ensemble transform data assimilation methods are suitable for the parameter estimation. For a small number of uncertain parameters, ensemble transform particle filter performs comparably to ensemble transform Kalman filter in terms of the mean estimation. For a large number of uncertain parameters, ensemble transform particle filter performs comparably to ensemble transform Kalman filter only when either localization or the leading modes are used