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This paper presents a comparison of two multi-fidelity methods for theforward uncertainty quantification of a naval engineering problem.Specifically, we consider the problem of quantifying the uncertainty of thehydrodynamic resistance of a roll-on/roll-off passengers ferry advancing incalm water and subject to two operational uncertainties (ship speed andpayload). The first four statistical moments (mean, variance, skewness,kurtosis), and the probability density function for such quantity of interest(QoI) are computed with two multi-fidelity methods, i.e., the Multi-IndexStochastic Collocation (MISC) method and an adaptive multi-fidelity StochasticRadial Basis Functions (SRBF) algorithm. The QoI is evaluated via computationalfluid dynamics simulations, which are performed with the in-house unsteadyReynolds-Averaged Navier-Stokes (RANS) multi-grid solver $\chi$navis. Thedifferent fidelities employed by both methods are obtained by stopping the RANSsolver at different grid levels of the multi-grid cycle. The performance ofboth methods are presented and discussed: in a nutshell, the findings suggestthat, at least for the current implementations of both algorithms, MISC couldbe preferred whenever a limited computational budget is available, whereas fora larger computational budget SRBFs seem to be preferable, thanks to itsrobustness to the numerical noise in the evaluations of the QoI.

Comparing Multi-Index Stochastic Collocation and Multi-Fidelity  Stochastic Radial Basis Functions for Forward Uncertainty Quantification of  Ship Resistance