A multi-fidelity polynomial chaos-greedy Kaczmarz approach for resource-efficient uncertainty quantification on limited budget

Abstract

Polynomial chaos expansion (PCE) has been widely used to facilitate uncertainty quantification and stochastic computations for complex systems. Multi-fidelity approaches expedite the construction of the PCE surrogate by blending the efficiency of low-fidelity models and accuracy of high-fidelity models. In this work, we propose a novel non-intrusive multi-fidelity sampling approach that exploits the low computational cost of the low-fidelity model to select a set of high-yield sampling locations for the high-fidelity model. Particularly, the proposed approach draws upon the unique features of the Kaczmarz updating scheme to design a greedy search that explores a large pool of low-fidelity samples and iteratively removes the least contributive ones. Facilitated via a subset updating strategy, the search lands on a small subset of the initial pool which is then used to construct the PCE surrogate for the high-fidelity model. The proposed approach offers a remarkable computational performance, practically delivering accurate results with a high-fidelity sample size about the cardinality of the basis, and as such is amenable to efficient uncertainty quantification on fixed and limited budget. We provide several numerical examples that demonstrate the promise of the proposed approach in substantially reducing the number of high-fidelity samples required for accurate construction of the PCE surrogate.