Multifidelity Modeling Using Nondeterministic Localized Galerkin Approach

Abstract

In this paper, multifidelity modeling using the new nondeterministic localized Galerkin approach is introduced to address the practical challenges associated with 1) multiple low-fidelity models, 2) localized correlations of low-fidelity models to a high-fidelity one, and 3) low-fidelity data or models under uncertainty. The proposed method employs two technical processes: the consolidation of multiple low-fidelity models and the refined adaptation of the consolidated model. Along with the resulting prediction model, the proposed method also provides model dominance information that can be used to understand the characteristic response of the high-fidelity model regarding essential behavior described by the low-fidelity models. Nondeterministic kriging is employed for variable-fidelity modeling under uncertainty. The performance and characteristics of the proposed method are demonstrated and discussed with multiple fundamental mathematical examples and a thermally coupled aircraft structural design problem. It is found that the proposed localized Galerkin multifidelity method can effectively deal with the practical challenges and provide an accurate prediction model with potential uncertainty bounds along with model dominance information.