Multi-fidelity surrogate-based parameter estimation for a sailing yacht hull

Given a numerical simulation m : ? 7? y_num, the objective of parameter estimation is to provide a joint posterior probability distribution p(?|y_exp) for an uncertain input parameter vector ? ? R^d, conditional on available experimental data y_exp ? R^q. However, exploring the posterior requires a high number of numerical simulations, which can make the problem impracticable within a given computational budget. A well-known approach to reduce the number of required simulations is to construct a surrogate, which - based on a set of training simulations - can provide a inexpensive approximation of the simulation output for any parameter configuration. To further reduce the total cost of the simulations, we can introduce low-fidelity as well as high-fidelity training simulations. In this case, a small number of expensive high-fidelity simulations is augmented with a larger number of inexpensive low-fidelity simulations. We investigate the scaling of the computational cost with the number of parameters, as well as the optimal ratio of the number of low-fidelity and high-fidelity training simulations.(Figure Presented) As an application we consider a towing tank experiment of the sailing yacht hull shown in Figure 1. The high-fidelity and low-fidelity simulations m_HF and m_LF solve the free-surface Reynolds-averaged Navier-Stokes equations on high and low-resolution grids, respectively. Experimental data y_exp are available for the resistance, sinkage and pitch over a range of Froude numbers. The uncertain parameters ? are the tank blockage, the mass and the centre of gravity. As a result we conclude that the centre of gravity is very close to the value provided by the laboratory, and that the tank blockage and mass are negatively correlated.