Surrogate-based Bayesian Comparison of Computationally Expensive Models: Application to Microbially Induced Calcite Precipitation

TL;DR

This paper introduces a surrogate-based Bayesian framework with correction factors for model comparison, enabling efficient evaluation of complex biogeochemical models like microbially induced calcite precipitation.

Contribution

It presents a novel approach combining polynomial chaos surrogates and correction factors to perform Bayesian model selection on computationally expensive geochemical models.

Findings

The method effectively compares models with reduced computational cost.

It quantifies the amount of data needed for reliable model selection.

The approach extends Bayesian justifiability analysis to complex biogeochemical processes.

Abstract

Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate one. Once observation data becomes available, a rigorous Bayesian model selection accompanied by a Bayesian model justifiability analysis could be employed to choose the most appropriate model, i.e. the one that describes the underlying physical processes best in the light of the available data. However, biogeochemical modeling is computationally very demanding because it conceptualizes different phases, biomass dynamics, geochemistry, precipitation and dissolution in porous media. Therefore, the Bayesian framework cannot be based directly on the full computational models as this would require too many expensive model evaluations. To circumvent this problem, we suggest performing both Bayesian model selection and justifiability analysis after constructing surrogates for the competing biogeochemical models. Here, we use the arbitrary polynomial chaos expansion. We account for the approximation error in the Bayesian analysis by introducing novel correction factors for the resulting model weights. Thereby, we extend the Bayesian justifiability analysis and assess model similarities for computationally expensive models. We demonstrate the method on a representative scenario for microbially induced calcite precipitation in a porous medium. Our extension of the justifiability analysis provides a suitable approach for the comparison of computationally demanding models and gives an insight on the necessary amount of data for a reliable model performance.