Adaptive N-Fidelity Metamodels for Noisy CFD Data

An adaptive #-fidelity approach to metamodeling from noisy data is presented for design-space exploration and design optimization. Computational fluid dynamics (CFD) simulations with different numerical accuracy (spatial discretization) provides metamodel training sets affected by unavoidable numerical noise. The #-fidelity approximation is built by an additive correction of a low-fidelity metamodel with metamodels of differences (errors) between higher-fidelity levels whose hierarchy needs to be provided. The approach encompasses two core metamodeling techniques, namely: i) stochastic radial-basis functions (SRBF) and ii) Gaussian process (GP). The adaptivity stems from the sequential training procedure and the auto-tuning capabilities of the metamodels. The method is demonstrated for an analytical test problem and a CFD-based optimization of a NACA airfoil, where the fidelity levels are defined by an adaptive grid refinement technique of a Reynolds-averaged Navier-Stokes (RANS) solver. The paper discusses: i) the effect of using more than two fidelity levels; ii) the use of least squares regression as opposed to exact interpolation; iii) the comparison between SRBF and GP; and iv) the use of two sampling approaches for GP. Results show that in presence of noise, the use of more than two fidelity levels improves the model accuracy with a significant reduction of the number of high-fidelity evaluations. Both least squares SRBF and GP provide promising results in dealing with noisy data.