Numerical models used in the design of floating bodies routinely rely on linear hydrodynamics. Extensions for hydrodynamic nonlinearities can be approximated using eg Morison type drag and nonlinear Froude-Krylov forces. This paper aims to improve the approximation of nonlinear forces acting on floating bodies by using machine learning (ML). Many ML models are general function approximators and therefore suitable for representing such nonlinear correction terms. A hierarchical modeling approach is used to build mappings between higher-fidelity simulations and the linear method. The ML corrections are built up for FNPF, Euler and RANS simulations. Results for decay tests of a sphere in model scale using recurrent neural networks (RNN) are presented. The RNN algorithm is shown to satisfactorily predict the correction terms if the most nonlinear case is used as training data. No difference in the performance of the RNN model is seen for the different hydrodynamic models.
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 modeling 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 an 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 introduces errors that propagate through the hierarchical modeling 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.