Multi-Fidelity, Gradient-enhanced, and Locally Optimized Sparse Polynomial Chaos and Kriging Surrogate Models Applied to Benchmark Problems

Abstract

In this paper, multi-fidelity, gradient-enhanced, and locally optimized sparse polynomial chaos expansion (PCE) and kriging surrogate models are constructed in lieu of solely using computationally expensive high-fidelity engineering analyses. Once an accurate surrogate model is built, it can be used for evaluating a large number of designs for design space exploration or for uncertainty quantification. To demonstrate that accurate multi-fidelity, gradient-enhanced, and locally optimized surrogate models can be obtained at lower computational cost than basic high-fidelity ones, a number of benchmark problems are employed. These include polynomial and non-polynomial analytical functions of arbitrary dimension, a heterogeneous non-polynomial analytical function in one, two, and three dimensions as well as a coupled spring-mass-system leading to a linear system of ODEs of arbitrary dimension.

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