Machine learning rather than trial and error to close morphodynamical tuneable parameters: application to a two-phase/two-layer model

Physics-based numerical models often depend on several parameters to close. Some of them can be expressed using established theoretical or empirical closure formulations. However, some others aggregate complex physical processes and are hence left as tuneable parameters, and can only be calibrated by trial and error. Yet, calibration data are not always available to do so, which prevents these models from being applied to wide ranges of laboratory or river flows. We hence propose a machine learning-based methodology to close any group of unclosed and correlated parameters, applied here to a two-phase/two-layer (2P2L) morphodynamical model. The methodology combines a numerical experiment with a known theoretical result and machine learning. It is applied to the considered model to close two friction parameters for which generalizable and vastly acknowledged closure formulations lack in the literature. The resulting hybrid model, combining the original 2P2L model and the closure models, is tested against two laboratory dam break test cases. Despite excessive smoothness and underestimation of the concentration in sediment, the hybrid model performed similarly to other models from the literature requiring trial and error calibration and showed high stability and accuracy regarding the estimation of the water-sediment mixture's inertia.