Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

Xiao, Cong; Tian, Leng

doi:10.1029/2019wr025366

Cited by 6 publications

(3 citation statements)

References 51 publications

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“…This is because the aperture fields generated from such a low‐dimensional latent space have little variance and are relatively smooth (i.e., low model complexity), as shown in the first row of Figures 7 and 8. After ES‐MDA, the 720 parameter sets collapse to the same posterior parameter set (Figure S1 in Supporting Information ), similar to the small ensemble size‐induced ensemble collapse phenomenon reported in many previous studies (Nejadi et al., 2017; Xiao & Tian, 2020). However, the simulation results from this posterior parameter set cannot correctly fit the “true” data (Figures 5a and 6a), which is an indicator of underfitting.…”

Section: Aperture Inversion and Thermal Prediction With Different Mod...supporting

confidence: 80%

“…Water Resources Research 10.1029/2023WR036146 collapse phenomenon reported in many previous studies (Nejadi et al, 2017;Xiao & Tian, 2020). However, the simulation results from this posterior parameter set cannot correctly fit the "true" data (Figures 5a and 6a), which is an indicator of underfitting.…”

Section: Comparison Between "True" and Simulated Tracer Pressure And ...mentioning

confidence: 81%

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Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

Wu,

Jin,

Jiang

et al. 2024

Water Resources Research

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A major challenge in the inversion of subsurface parameters is the ill‐posedness issue caused by the inherent subsurface complexities and the generally spatially sparse data. Appropriate simplifications of inversion models are thus necessary to make the inversion process tractable and meanwhile preserve the predictive ability of the inversion results. In this study, we investigate the effect of model complexity on fracture aperture inversion and thermal performance prediction in a field‐scale EGS model. Principal component analysis was used to map the aperture field to a low‐dimensional latent space. The complexity of the inversion model was quantitatively represented by the percentage of total variance in the original aperture fields preserved by the latent space. Tracer, pressure and flow rate data were used to invert for fracture aperture through an ensemble‐based inversion method, and the inferred aperture field was used to predict thermal performance. With an over‐simplified aperture model, ensemble collapse occurred. The inverted aperture models failed to resolve necessary flow and transport features, leading to a biased thermal performance prediction. A complex aperture model involved excessive features and was prone to overinterpreting the inversion data. Both the tracer/pressure/flow rate data reproduction and thermal prediction showed significant uncertainties, making it difficult to properly estimate long‐term thermal performance. Fortunately, our results indicate that there exists an appropriate model complexity which can simultaneously match inversion data and predict thermal performance with an acceptable uncertainty. The quality of the fit of tracer data appears to be a useful indicator of such an appropriate model complexity.

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Section: Aperture Inversion and Thermal Prediction With Different Mod...supporting

confidence: 80%

Section: Comparison Between "True" and Simulated Tracer Pressure And ...mentioning

confidence: 81%

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

Wu,

Jin,

Jiang

et al. 2024

Water Resources Research

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show abstract

“…Therefore, only the field within the inscribed circle of the generated 800 m × 800 m aperture field is used for flow, tracer and thermal simulation. S1 in the Supporting Information), similar to the small ensemble size-induced ensemble collapse phenomenon reported in many previous studies (Nejadi et al, 2017;Xiao & Tian, 2020). However, the simulation results from this posterior parameter set cannot correctly fit the "true" data (Figs.…”

Section: Parameterizationsupporting

confidence: 79%

Selecting appropriate model complexity: An example of tracer inversion for thermal prediction in enhanced geothermal systems

Jin

et al. 2022

Preprint

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A major challenge in the inversion of subsurface parameters is the ill-posedness issue caused by the inherent subsurface complexities and the generally spatially sparse data. Appropriate simplifications of inversion models are thus necessary to make the inversion process tractable and meanwhile preserve the predictive ability of the inversion results. In the present study, we investigate the effect of model complexity on the inversion of fracture aperture distribution as well as the prediction of longterm thermal performance in a field-scale single-fracture EGS model. Principal component analysis (PCA) was used to map the original cell-based aperture field to a low-dimensional latent space. The complexity of the inversion model was quantitatively represented by the percentage of total variance in the original aperture fields preserved by the latent space. Tracer, pressure and flow rate data were used to invert for fracture aperture through an ensemble-based inversion method, and the inferred aperture field was then used to predict thermal performance. We found that an over-simplified aperture model could not reproduce the inversion data and the predicted thermal response was biased. A complex aperture model could reproduce the data but the thermal prediction showed significant uncertainty. A model with moderate complexity, although not resolving many fine features in the "true" aperture field, successfully matched the data and predicted the long-term thermal behavior. The results provide important insights into the selection of model complexity for effective subsurface reservoir inversion and prediction.

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An adaptive multi-fidelity optimization framework based on co-Kriging surrogate models and stochastic sampling with application to coastal aquifer management

Christelis,

Kopsiaftis,

Regis

et al. 2023

Advances in Water Resources

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Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

Cited by 6 publications

References 51 publications

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

Selecting appropriate model complexity: An example of tracer inversion for thermal prediction in enhanced geothermal systems

An adaptive multi-fidelity optimization framework based on co-Kriging surrogate models and stochastic sampling with application to coastal aquifer management

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