A Surrogate-Assisted Uncertainty-Aware Bayesian Validation Framework and its Application to Coupling Free Flow and Porous-Medium Flow

• Published in: arXiv.org
• Main Authors: Mohammadi, Farid, Eggenweiler, Elissa, Flemisch, Bernd, Oladyshkin, Sergey, Rybak, Iryna, Schneider, Martin, Weishaupt, Kilian
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.06.2022
• Subjects: Bayesian analysis; Benchmarks; Computational fluid dynamics; Coupling; Darcys law; Fluid flow; Free flow; Mathematical models; Model reduction; Parameter uncertainty; Polynomials; Porous media; Statistical analysis

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid--porous interface. These models include a porous-medium model using Darcy's law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems' behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model's predictive capabilities, and make a probabilistic model comparison.