Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

Köppel, Markus; Franzelin, Fabian; Kröker, Ilja; Oladyshkin, Sergey; Santin, Gabriele; Wittwar, Dominik; Barth, Andrea; Haasdonk, Bernard; Nowak, Wolfgang; Pflüger, Dirk; Rohde, Christian

doi:10.1007/s10596-018-9785-x

Cited by 30 publications

(36 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In more general terms, other aspects of model‐ and data‐driven surrogate modelling could be investigated. For instance, the same kernel‐based technique has been recently applied to uncertainty quantification . In the present setting, this could lead to the fast assessment of the impact of uncertainty on the model output, e.g., in a setting where the stenosis degree or other possible input quantities are not exactly measured.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

Köppl

Santin

Haasdonk

et al. 2018

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

In this work, we consider 2 kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery, i.e., in an artery that is located far away from the heart. For our simulations, we place the stenosis in one of the tibial arteries belonging to the right lower leg (right posterior tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-D and 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrised by the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore, it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model.

show abstract

Section: Conclusion and Further Workmentioning

confidence: 99%

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

Köppl

Santin

Haasdonk

et al. 2018

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…The CO 2 injection into the subsurface could be a possible practice to mitigate the CO 2 emission into the atmosphere. In this study, we use the deterministic model, provided by Köppel et al [ 24 ], which is a reduced version of the model in a benchmark problem defined in the paper [ 85 ]. This reduction consists of a radial flow in the vicinity of the injection well, and made primarily due to the high computational demand of the original CO 2 model.…”

Section: Application Of Gpe-based Bayesian Active Learningmentioning

confidence: 99%

“…Overall, the considered CO 2 benchmark problem is strongly nonlinear because the CO 2 saturation spreaders as a strongly nonlinear front that could be challenging to capture via surrogates. For detailed information on the governing equations, the modeling assumption and the approaches, the reader is referred to the original publication [ 24 ].…”

Section: Application Of Gpe-based Bayesian Active Learningmentioning

confidence: 99%

“…Similar to [ 24 ], we consider the combined effects of three sources of uncertainty. We take into account the uncertainty of boundary conditions due to the injection rate, the uncertainty of parameters in the constitutive relations, introduced via uncertainty in the relative permeability definitions, and the uncertainty of material properties, i.e., the porosity of the geological layer.…”

Section: Application Of Gpe-based Bayesian Active Learningmentioning

confidence: 99%

“…GPEs also offer representation via various kernels, and have gained popularity for such machine learning tasks as classification [ 22 ] and regression problems [ 23 ]. A recent paper [ 24 ] compares various surrogate-based approaches using a common benchmark model for forward uncertainty quantification in carbon carbon dioxide storage.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian3 Active Learning for the Gaussian Process Emulator Using Information Theory

Oladyshkin

Mohammadi

Kroeker

et al. 2020

Entropy

Self Cite

View full text Add to dashboard Cite

Gaussian process emulators (GPE) are a machine learning approach that replicates computational demanding models using training runs of that model. Constructing such a surrogate is very challenging and, in the context of Bayesian inference, the training runs should be well invested. The current paper offers a fully Bayesian view on GPEs for Bayesian inference accompanied by Bayesian active learning (BAL). We introduce three BAL strategies that adaptively identify training sets for the GPE using information-theoretic arguments. The first strategy relies on Bayesian model evidence that indicates the GPE’s quality of matching the measurement data, the second strategy is based on relative entropy that indicates the relative information gain for the GPE, and the third is founded on information entropy that indicates the missing information in the GPE. We illustrate the performance of our three strategies using analytical- and carbon-dioxide benchmarks. The paper shows evidence of convergence against a reference solution and demonstrates quantification of post-calibration uncertainty by comparing the introduced three strategies. We conclude that Bayesian model evidence-based and relative entropy-based strategies outperform the entropy-based strategy because the latter can be misleading during the BAL. The relative entropy-based strategy demonstrates superior performance to the Bayesian model evidence-based strategy.

show abstract

Hierarchical Extended B-splines for Approximations on Sparse Grids

Rehme

Zimmer

Pflüger

2021

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

Cited by 30 publications

References 57 publications

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods

Bayesian3 Active Learning for the Gaussian Process Emulator Using Information Theory

Hierarchical Extended B-splines for Approximations on Sparse Grids

Contact Info

Product

Resources

About