A Hierarchical multi-fidelity approach for Bayesian inference for numerical process simulations

A key prerequisite for reliable geoscientific process simulations is the calibration of uncertain model parameters against field observations. In practice, both measurements and simulation outputs are subject to uncertainty, arising from the observational errors, limited knowledge of material properties and inexact physical models. Bayesian inference provides a framework to explicitly acknowledge multiple sources of uncertainty by encoding modelling assumptions in prior distributions and updating them against observational data through the likelihood to obtain posterior estimates. However, applying Bayesian methods remains challenging in coupled multiphysical applications, including thermo-hydro-mechanical problems, as computational costs of repeated forward evaluations grow rapidly with model complexity.  

To address these limitations, we develop a hierarchical simulator for Bayesian calibrations that dynamically combines fast low-fidelity surrogate models with accurate high-fidelity finite-element simulations during the sampling stage. The core of the method stems from a fidelity-selection policy embedded directly in the probabilistic model, which transparently accounts for both surrogate-induced bias and the computational cost associated with high-fidelity simulations. We provide and compare several scenarios, that represent different optimization strategies for balancing posterior accuracy and computational efficiency. The resulting hierarchical Bayesian workflow is highly modular, and it can be coupled with external high-fidelity solvers through a unified forward interface and hence applicable to a wider range of geoscientific problems.