A unified Bayesian model selection workflow for geophysical free-surface flow

The broad family of shallow flow models arises from depth-averaging the underlying governing balance laws. Depth-averaging yields an analytical model complexity reduction, increasing computational efficiency and reducing the number of model parameters. Consequently, shallow flow models become a desirable choice for various scientific and engineering applications, such as landslide prediction and coastal engineering. In the realm of landslide modelling, different variants of shallow flow models are often tailored - sometimes in an ad hoc manner - to specific physical phenomena, such as basal shear, non-hydrostatic effects, kinetics, or phase change processes. Therefore, selecting the most appropriate shallow flow model for a particular scenario based on quantitative reasoning poses a formidable challenge. Quantifying the uncertainty associated with this model selection is essential to assess the reliability of the predictions of these shallow flow models.

Here, we present a unified Bayesian model selection workflow leveraging Gaussian Process emulation — a machine learning technique used for non-intrusive physics-based machine learning. It starts with model calibration, where we generate posterior samples. These are then used to calculate the marginal likelihood, the basis for our model selection. This process faces two computational bottlenecks: significant computational costs involved in numerous model evaluations during calibration and high-dimensional, intractable integrals in the computation of Marginal Likelihood. To address the former, we integrated Gaussian process emulators into the workflow using PSimPy, our in-house Python package, for predictive and probabilistic simulations. For the latter bottleneck, we conducted a comprehensive literature review, with particular emphasis on marginal likelihood computation techniques based on Importance Sampling and implemented single proposal density schemes and integrated them into the workflow.

We demonstrate our approach using elementary landslide runout models across varying fidelity levels, investigating the impact of data representation—specifically, comparing point data to time series data—while considering data characteristics such as velocity and distance. Additionally, we calibrated the discrepancy parameter for robust handling of uncertainties associated with the data. Our future work will focus on implementing advanced importance sampling schemes to enhance the computation of the Marginal Likelihood, especially in high-dimensional scenarios. Furthermore, emphasis will be placed on adopting a hierarchical approach to address data uncertainty in conjunction with model inadequacy, which is not accounted for in the existing workflow.