Overcoming the Model‐Data‐Fit Problem in Porous Media: A Quantitative Method to Compare Invasion‐Percolation Models to High‐Resolution Data

Banerjee, Ishani; Guthke, Anneli; Ven, Cole J.C. Van De; Mumford, Kevin G.; Nowak, Wolfgang

doi:10.1029/2021wr029986

Cited by 2 publications

(11 citation statements)

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“…Macro-Invasion Percolation (Macro-IP) models are an upscaled abstraction of pore-scale IP models. We have used a Macro-IP model with the experimental data used in this study in a previous study [24]. The SIP model is conceptually similar to the Macro-IP model of [24].…”

Section: Demonstration On a Real Case Studymentioning

confidence: 99%

“…We have used a Macro-IP model with the experimental data used in this study in a previous study [24]. The SIP model is conceptually similar to the Macro-IP model of [24]. The difference between the SIP model and the Macro-IP model of [24] is an additional rule for stochastic selection from the Stochastic Selection and Invasion (SSI) model of [33].…”

Section: Demonstration On a Real Case Studymentioning

confidence: 99%

“…The SIP model is conceptually similar to the Macro-IP model of [24]. The difference between the SIP model and the Macro-IP model of [24] is an additional rule for stochastic selection from the Stochastic Selection and Invasion (SSI) model of [33]. Thus, to describe the SIP model, we describe the model formulation of the Macro-IP model [24] and the additional rule for stochastic selection in Section 3.1.…”

Section: Demonstration On a Real Case Studymentioning

confidence: 99%

“…Further, our method can be used in combination with all reduced-order modelling approaches that maintain the Markov property. Other options include an abstraction of summary statistics from data (so-called approximate Bayesian computation [22]), manual-visible techniques (like moments matching [23]), or the use of plausible, non-Bayesian metrics [24].…”

Section: Introductionmentioning

confidence: 99%

“…Further, we add a list of general algorithmic steps of MFP in Section 3.5. In a previous study [24], we used the (Diffused) Jaccard coefficient to facilitate a quantitative comparison of an invasion percolation model to the experimental data set used in this study. This technique only works on image-type data and is not free from information losses.…”

Section: Introductionmentioning

confidence: 99%

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The method of forced probabilities: a computation trick for Bayesian model evidence

et al. 2022

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Bayesian model selection objectively ranks competing models by computing Bayesian Model Evidence (BME) against test data. BME is the likelihood of data to occur under each model, averaged over uncertain parameters. Computing BME can be problematic: exact analytical solutions require strong assumptions; mathematical approximations (information criteria) are often strongly biased; assumption-free numerical methods (like Monte Carlo) are computationally impossible if the data set is large, for example like high-resolution snapshots from experimental movies. To use BME as ranking criterion in such cases, we develop the “Method of Forced Probabilities (MFP)”. MFP swaps the direction of evaluation: instead of comparing thousands of model runs on random model realizations with the observed movie snapshots, we force models to reproduce the data in each time step and record the individual probabilities of the model following these exact transitions. MFP is fast and accurate for models that fulfil the Markov property in time, paired with high-quality data sets that resolve all individual events. We demonstrate our approach on stochastic macro-invasion percolation models that simulate gas migration in porous media, and list additional examples of probable applications. The corresponding experimental movie was obtained from slow gas injection into water-saturated, homogeneous sand in a 25 x 25 x 1 cm acrylic glass tank. Despite the movie not always satisfying the high demands (resolving all individual events), we can apply MFP by suggesting a few workarounds. Results confirm that the proposed method can compute BME in previously unfeasible scenarios, facilitating a ranking among competing model versions for future model improvement.

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Section: Demonstration On a Real Case Studymentioning

confidence: 99%