All-at-once approach to multifidelity polynomial chaos expansion surrogate modeling

A new approach to multifidelity, gradient-enhanced surrogate modeling using polynomial chaos expansions is presented. This approach seeks complementary additive and multiplicative corrections to low fidelity data whereas current hybrid methods in the literature attempt to balance individually calculated calibrations. An advantage of the new approach is that least squares-optimal coefficients for both corrections and the model of interest are determined simultaneously using the high-fidelity data directly in the final surrogate. The proposed technique is compared to the weighted approach for three analytic functions and the numerical simulation of a vehicle's lift coefficient using Cartesian Euler CFD and panel aerodynamics. Investigation of the individual correction terms indicates the advantage of the proposed approach is that complementary calibrations separately adjust the low-fidelity data in local regions based on agreement or disagreement between the two fidelities. In cases where polynomials are suitable approximations to the true function, the new all-at-once approach is found to reduce error in the surrogate faster than the method of weighted combinations. When the low-fidelity is a good approximation of the true function, the proposed technique out-performs monofidelity approximations as well. Sparse grid constructions alleviate the growth of the training set as root-mean-square-error is calculated for increasingly higher polynomial orders. Utilizing gradient information provides an advantage at lower training grid levels for low-dimensional spaces, but worsens numerical conditioning of the system in higher dimensions. Published by Elsevier Masson SAS.