Certified reduced basis method in geosciences

Degen, Denise; Veroy, Karen; Wellmann, Florian

doi:10.1007/s10596-019-09916-6

Cited by 24 publications

(26 citation statements)

References 34 publications

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“…This stage is computationally fast and therefore ideal for expensive outer loop processes such as the global sensitivity analysis. In previous studies, we showed that the RB method yields a speed-up of several orders of magnitude for the here described physical problem (Degen et al, 2020b, a).…”

Section: Reduced Order Modelingmentioning

confidence: 73%

“…The reduced basis method is widely known in mathematical applications (i.e. Benner et al, 2015;Grepl, 2005;Hesthaven et al, 2016;Aretz-Nellesen et al, 2019;Kärcher et al, 2018;Prud'homme et al, 2002;Quarteroni et al, 2015;Rozza et al, 2007), however only few geoscientific applications exist (Degen et al, 2020b). Nevertheless, some studies do use comparable approaches (Ghasemi and Gildin, 2016;Gosses et al, 2018;Rizzo et al, 2017;Rousset et al, 2014;Zlotnik et al, 2015).…”

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confidence: 99%

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How biased are our models? – A Case Study of the Alpine Region

Degen

Spooner

Scheck‐Wenderoth

et al. 2021

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Abstract. Geophysical process simulations play a crucial role in the understanding of the subsurface. This understanding is required to provide, for instance, clean energy sources such as geothermal energy. However, the calibration and validation of the physical models heavily rely on state measurements such as temperature. In this work, we demonstrate that focusing analyses purely on measurements introduces a high bias. This is illustrated through global sensitivity studies. The extensive exploration of the parameter space becomes feasible through the construction of suitable surrogate models via the reduced basis method, where the bias is found to result from very unequal data distribution. We propose schemes to compensate for parts of this bias. However, the bias cannot be entirely compensated. Therefore, we demonstrate the consequences of this bias with the example of a model calibration.

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Section: Reduced Order Modelingmentioning

confidence: 73%

mentioning

confidence: 99%

How biased are our models? – A Case Study of the Alpine Region

Degen

Spooner

Scheck‐Wenderoth

et al. 2021

Preprint

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“…We generate all reduced models with the software package DwarfElephant (Degen et al, 2020b). DwarfElephant is based on the Multiphysics Object-Oriented Simulation Environment (MOOSE), a state-of-the-art finite element solver primarily developed by the Idaho National Laboratory (Alger et al, 2019).…”

Section: Surrogate Model Constructionmentioning

confidence: 99%

“…The RB method is a Model Order Reduction (MOR) technique that aims at significantly reducing the spatial and temporal degrees of freedom of, as applied in this study, finite element problem formulations. The RB method has been widely studied by, for example, Grepl and Patera (2005);Hesthaven et al (2016);Prud'homme et al (2002); Quarteroni et al (2015) for mathematical benchmark examples, and for the first time by Degen et al (2020b) in a geoscientific context. In this study, we make use of the RB method to guide the construction of the surrogate model since it allows, in contrast to other statistical methods including Kriging and response surfaces (Baş and Boyacı, 2007;Bezerra et al, 2008;Frangos et al, 2010;Khuri and Mukhopadhyay, 2010;Miao et al, 2019;Mo et al, 2019;Myers et al, 2016;Navarro et al, 2018), the retrieval of the entire state variable (i.e.…”

Section: Introductionmentioning

confidence: 99%

Effects of Transient Processes for Thermal Simulations of the Central European Basin

Degen¹,

Cacace²

2020

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Abstract. Transient processes play a major role in geophysical applications. In this paper, we quantify the significant influence arising from transient processes for conductive heat transfer problems for sedimentary basin systems. We demonstrate how the thermal properties are affected by changing the system from a stationary to a non-stationary system and what impact transient boundary conditions (derived from paleoclimate information) have. Furthermore, we emphasize the importance of time-stepping approaches and the simulation duration since both factors influence the sensitivities of the thermal properties. We employ global sensitivity analyses to quantify not only the impact arising from the thermal properties but also their parameter correlations. Furthermore, we show how the results of the sensitivity analysis can be used to gain further insights into the complex Central European Basin System. This computationally very demanding workflow becomes feasible through the construction of high precision surrogate models using the reduced basis method.

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“…This method has been adapted successfully for geophysical simulations (Degen et al, 2020) and showed promising results with a reduction of simulation time by several orders of magnitude, after model training, while still providing highly accurate estimates of state variables at measurement locations. We will apply this method here to make a global SA feasible and to efficiently test several model scenarios.…”

Section: Introductionmentioning

confidence: 99%

Global Sensitivity Analysis to Optimize Basin-Scale Conductive Model Calibration – A Case Study From the Upper Rhine Graben

Degen¹,

Veroy²,

Freymark³

et al. 2020

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Geothermal simulations are widely used in both scientific and applied industrial contexts. Typically, the temperature state is evaluated on the basis of the heat equation, with suitable parameterizations of the model domain and defined boundary conditions, which are calibrated to obtain a minimal misfit between measured and simulated temperature values. We demonstrate the essential need for global sensitivity studies for robust geothermal model calibrations since local studies overestimate the influence of the parameters. We ensure the feasibility of the study by using a physics-based machine learning approach, that reduces the computation time by several orders of magnitude.

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Certified reduced basis method in geosciences

Cited by 24 publications

References 34 publications

How biased are our models? – A Case Study of the Alpine Region

How biased are our models? – A Case Study of the Alpine Region

Effects of Transient Processes for Thermal Simulations of the Central European Basin

Global Sensitivity Analysis to Optimize Basin-Scale Conductive Model Calibration – A Case Study From the Upper Rhine Graben

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