Bayesian model selection under computational time constraints: application to river modeling

Bayesian model selection (BMS) provides objective guidance in how to select the most appropriate model for a specific modeling goal. Its applicability is however limited by high computational costs. To transfer it to computationally expensive modeling tasks, we combine BMS and model reduction. Accounting for the approximation error in the reduced model, we introduce a novel correction factor yielding a model ranking that is (more) representative of the full-complexity models.

We demonstrate our proposed approach on hydro-morphodynamic modeling of a 10-km stretch of the lower Rhine river in Germany. Sediment transport and river bed evolution is predicted with four commonly used sediment transport formulas (Meyer-Peter and Müller, Hunziker, van Rijn, and Wu). With only a very limited number of full-complexity model runs, we build response surfaces via the so-called arbitrary Polynomial Chaos Expansion (aPC) to approximate the four competing model variants. Based on measurement data provided by the Federal Waterways Research Institute (BAW) in Karlsruhe, Germany, we obtain a Bayesian ranking of the four reduced models. This ranking is then corrected in view of the different approximation quality achieved by the individual reduced models. Results show that this correction factor shields us from misleading model ranking outcomes.

Equipped with the proposed correction factor, the Bayesian model selection framework provides valuable guidance in choosing among computationally expensive models for river engineering or any other geoscience modeling task.