Multi-fidelity approach to Bayesian parameter estimation in subsurface heat and fluid transport models

Area of Science:

• Geosciences
• Computational Modeling
• Environmental Engineering

Background:

• Urban subsurface utilization for infrastructure and geothermal energy necessitates advanced coupled mass and heat transfer models.
• Large-scale models face significant uncertainties in parameters, model structure, and sparse data, hindering reliability.
• Parameter estimation and model calibration are computationally intensive, posing a challenge for complex models.

Purpose of the Study:

• To develop a novel Bayesian approach for robust parameter estimation in large-scale coupled subsurface models.
• To address uncertainties, sparse data, and computational burdens associated with subsurface modeling.
• To optimize the use of computational resources by integrating multi-fidelity model outputs.

Main Methods:

• A Bayesian framework was developed to incorporate uncertainties and sparse field data.
• Multi-fidelity modeling was employed, combining outputs from models with varying spatial resolutions.
• Gaussian Process models were used to emulate model discrepancies and biases for efficient re-iteration.

Main Results:

• The novel multi-fidelity Bayesian approach significantly improved parameter estimation accuracy and precision compared to single-fidelity methods.
• The framework successfully handled sparse data and accounted for various uncertainty sources.
• Assessment of model bias and inter-fidelity discrepancies was enabled through the Bayesian error terms.

Conclusions:

• The proposed multi-fidelity Bayesian approach offers a robust and efficient solution for parameter estimation in complex subsurface modeling.
• This method enhances the reliability of subsurface models for applications like geothermal energy and urban infrastructure development.
• Gaussian Process emulation allows for iterative refinement of parameter estimates without requiring additional expensive numerical simulations.