Optimization of 2d hydrodynamic model roughness with multioutput Gaussian process emulators and Bayesian active learning

This study presents a metamodeling approach using multioutput Gaussian process emulators (MO-GPEs) within a Bayesian active learning (BAL) framework to optimise spatially varying Nikuradse roughness coefficients in a 2d hydrodynamic model. The approach is applied in a near-natural fishway with a gravel bed. MO-GPEs learn relationships among deterministic numerical model outputs and are used in BAL to emulate response surfaces of complex physics-based models and iteratively select informative training points conditioned on measured data. This supervised learning procedure is showcased herein by means of a simultaneous Bayesian calibration of four Nikuradse roughness coefficients, and it provides uncertainty quantifications of these calibration parameters. The results show a reduction of 4.5% in normalised-root mean square error compared to a first-principle-reasoned benchmark model simulated with a global model roughness value. The uncertainty, measured by the width of posterior distributions, also reduces for all four calibrated roughness coefficients, indicating a more constrained high-probability region.