Regularized ensemble Kalman methods for inverse problems

Zhang, Xinlei; Ströfer, Carlos A. Michelén; Xiao, Heng

doi:10.1016/j.jcp.2020.109517

Cited by 46 publications

(29 citation statements)

References 44 publications

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“…We remark that this method is based on the solution of adjoint problems to compute the gradient, which may not be available in any CFD code (even though automatic difference tools become more and more standard nowadays, see for example Economon et al [41]). For this reason, we point out that regularized ensemble-based data assimilation methods may also be used for solving inverse problems [42,43].…”

Section: Minimal Momentum Force Correction (Output) Of Rans Model By ...mentioning

confidence: 99%

Machine learning-augmented turbulence modeling for RANS simulations of massively separated flows

et al. 2021

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Most widely used Reynolds-Averaged Navier-Stokes (RANS) models employ the Boussinesq approximation, which assumes a linear relationship between the turbulent Reynolds stresses and the mean-velocity gradient tensor. This assumption, which can be very stringent, is more suited for simple shear-flows and is regarded as an important shortcoming for the improvement of the representation of turbulence in complex geometries. Correction of the local turbulence length scales, as achieved for example by the introduction of a correction term in the eddy-viscosity equation of a Spalart-Allmaras model, then indeed only allows relatively small corrections to the base-line model and may not be sufficiently flexible to adapt to common situations where the Reynolds stresses are not aligned with the velocity gradient tensor. For the variational data-assimilation step, we consider a vectorial source correction term in the momentum equations (output quantity) together with the Spalart-Allmaras model, which allows full flexibility to adapt to any mean-flow topology. We show how the machine-learning framework should be adapted, in particular with respect to the vectorial nature of the correction term and given invariance properties. As for the input quantities, we discuss the impact of considering either local quantities for the non-dimensionalization or global ones that characterize the configuration. We showcase the procedure on the periodic hill configuration, for which a rich DNS database is available in the literature: in particular, availability of the full mean-flow solution for a range of Reynolds numbers and geometries, ensures identification of "physical" correction terms and allows learning of turbulence models that accurately extrapolate to new Reynolds numbers and geometries.

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Section: Minimal Momentum Force Correction (Output) Of Rans Model By ...mentioning

confidence: 99%

Machine learning-augmented turbulence modeling for RANS simulations of massively separated flows

et al. 2021

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“…Panel (h) represents the hypothetical true field of λ et al 27 The second selection method is based on the magnitudes of KL eigenvalues, which indicate the intrinsic importance of corresponding KL modes. 54 If the λ field inferred from two selection methods are similar, the second selection method may be preferred since no extra sensitivity analysis and corresponding forward model evaluations are needed. It should be noted that the selected variables are different in two selection methods but the number of selected variables should be the same.…”

Section: Inversion Schemesmentioning

confidence: 99%

Bayesian inference of spatially varying parameters in soil constitutive models by using deformation observation data

Tao

Sun

Cai

2021

Num Anal Meth Geomechanics

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Parameters of soil constitutive models are usually identified through laboratory tests. The spatial variability of these parameters is generally not considered due to the limitation of the test scale. This study proposes a data-driven approach to infer the spatially varying parameter of the modified Cam-clay model from limited field observations and subsequently improves soil settlement predictions. The observation data and numerical results of random finite element method are assimilated in an inverse modeling process based on the iterative Ensemble Kalman filtering (iEnKF). Different unknown variables and number of observations are used to study their effects on parameter estimations and settlement predictions. The effectiveness of the proposed approach is illustrated through a synthetic partial-loading test. The results show that the site-specific spatial variability can be estimated reasonably, and predictions of settlement can be improved by using the inferred parameter field. When the variables to be inferred change from all 60 variables to the selected 17 important variables, the average error of the estimated fields increases, but the variance decreases. A reduction in the observation spacing and an increase in the number of observations lead to a slightly smaller error of the mean and considerably reduced uncertainties of soil parameters. Although the inferred results of parameter field show different accuracies, the corresponding calculated settlements are generally similar and satisfactory.

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“…However, when nonlinearity is present in the constraints, more sophisticated strategies are needed, similar to the situation of handling nonlinearity in unconstrained data assimilation problems. Such strategies include, e.g., the first or second order linearization of a nonlinear-constraint system [13,15,35,42,44], unscented transform [39,41], particle approximation [43], moving horizon estimation [3], iterative approximation [9], and their combinations.…”

Section: Introductionmentioning

confidence: 99%

“…We recast data assimilation with constraints as a constrained optimization problem. However, instead of relying on a general-purpose numerical optimization algorithm to solve the constrained optimization problem, we derive an (approximate) closed form for model update, but without the need to explicitly linearize the constraint systems, in contrast to some recently proposed ensemble-based algorithms (e.g., [13,15,44]) to handle nonlinear constraints. This closed form bears similarities to the model update formula of an ordinary iterative ensemble smoother (IES) [8,11,25] applied to unconstrained data assimilation problems.…”

Section: Introductionmentioning

confidence: 99%

Data assimilation with soft constraints (DASC) through a generalized iterative ensemble smoother

Luo

Cruz

2022

Comput Geosci

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This work investigates an ensemble-based workflow to simultaneously handle generic, nonlinear equality and inequality constraints in reservoir data assimilation problems. The proposed workflow is built upon a recently proposed umbrella algorithm, called the generalized iterative ensemble smoother (GIES), and inherits the benefits of ensemble-based data assimilation algorithms in geoscience applications. Unlike the traditional ensemble assimilation algorithms, the proposed workflow admits cost functions beyond the form of nonlinear-least-squares, and has the potential to develop an infinite number of constrained assimilation algorithms. In the proposed workflow, we treat data assimilation with constraints as a constrained optimization problem. Instead of relying on a general-purpose numerical optimization algorithm to solve the constrained optimization problem, we derive an (approximate) closed form to iteratively update model variables, but without the need to explicitly linearize the constraint systems. The established model update formula bears similarities to that of an iterative ensemble smoother (IES). Therefore, in terms of theoretical analysis, it becomes relatively easy to transit from an ordinary IES to the proposed constrained assimilation algorithms, and in terms of practical implementation, it is also relatively straightforward to implement the proposed workflow for users who are familiar with the IES, or other conventional ensemble data assimilation algorithms like the ensemble Kalman filter (EnKF). Apart from the aforementioned features, we also develop efficient methods to handle two noticed issues that would be of practical importance for ensemble-based constrained assimilation algorithms. These issues include localization in the presence of constraints, and the (possible) high dimensionality induced by the constraint systems. We use one 2D and one 3D case studies to demonstrate the performance of the proposed workflow. In particular, the 3D example contains experiment settings close to those of real field case studies. In both case studies, the proposed workflow achieves better data assimilation performance in comparison to the choice of using an original IES algorithm. As such, the proposed workflow has the potential to further improve the efficacy of ensemble-based data assimilation in practical reservoir data assimilation problems.

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Regularized ensemble Kalman methods for inverse problems

Cited by 46 publications

References 44 publications

Machine learning-augmented turbulence modeling for RANS simulations of massively separated flows

Machine learning-augmented turbulence modeling for RANS simulations of massively separated flows

Bayesian inference of spatially varying parameters in soil constitutive models by using deformation observation data

Data assimilation with soft constraints (DASC) through a generalized iterative ensemble smoother

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