Hierarchical Approaches to Train Recurrent Neural Networks for Wave-Body Interaction Problems

We present a hybrid linear potential flow - machine learning (LPF-ML) model for simulating weakly nonlinear wave-body interaction problems. In this paper we focus on using hierarchical modelling for generating training data to be used with recurrent neural networks (RNNs) in order to derive nonlinear correction forces. Three different approaches are investigated: (i) a baseline method where data from a Reynolds averaged Navier Stokes (RANS) model is directly linked to data from a LPF model to generate nonlinear corrections; (ii) an approach in which we start from high-fidelity RANS simulations and build the nonlinear corrections by stepping down in the fidelity hierarchy; and (iii) a method starting from low-fidelity, successively moving up the fidelity staircase. The three approaches are evaluated for the simple test case of a heaving sphere. The results show that the baseline model performs best, as expected for this simple test case. Stepping up in the fidelity hierarchy very easily introduce errors that propagate through the hierarchical modelling via the correction forces. The baseline method was found to accurately predict the motion of the heaving sphere. The hierarchical approaches struggled with the task, with the approach that steps down in fidelity performing somewhat better of the two.