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

Abstract

Given a numerical simulation m : ξ → y num , the objective of parameter estimation is to provide a joint posterior probability distribution p(ξ|y exp) for an uncertain input parameter vector ξ ∈ 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, whichbased 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.