Multi-fidelity surrogate modelling with polynomial chaos expansions

Abstract

In this master thesis we aim at exploring the field of multi-fidelity surrogate modelling with polynomial chaos expansions (PCE). First we give an overview of the historical development of multi-fidelity surrogate modelling and surrogate modelling in general. Then we present the state-of-the-art techniques for multi-fidelity PCE, such as the additive correction, multiplicative correction and combined additive and multiplicative correction methods; these methods are all based on the concept of model discrepancy. Afterwards we propose the spectral recombination approach to multi-fidelity surrogate modelling with polynomial chaos expansions. The proposed optimal weights recombination approach tries to find the optimal recombination of the high-fidelity and low-fidelity polynomial coefficients using an objective error measure, e.g. the normalized empirical error. For all methods presented in the thesis we use regression, e.g. LARS, to calculate the polynomial coefficients. To test the techniques proposed, we apply the presented methods on a variety of analytical test functions as well as a real-world engineering problem. We use the relative estimation of the mean / variance and the normalized empirical error to compare the performance of the different methods presented. We show that for analytical test functions, the additive correction technique often achieves improvements in the estimate of mean and variance when compared to a PCE model built using only the high-fidelity experimental design. On the contrary, when applied to a real-world engineering problem the additive correction techniques provides unsatisfactory results. The optimal weight recombination method provides smaller reductions of the error measures considered when applied to analytical test functions. However, for the wind turbine case study, the optimal weights recombination method provides the largest reduction of the normalized empirical error compared to the high-fidelity PCE.

Keywords

Multi-fidelity, Polynomial Chaos Expansion, Sparse PCE, Surrogate Modelling, Compressive Sensing, Least Angle Regression, LARS, Spectral recombination

BibTeX cite

MSCTHESIS{MBerchierThesis,
author = {Berchier, M.},
title = {MULTI-FIDELITY SURROGATE MODELLING WITH POLYNOMIAL CHAOS EXPANSIONS},
school = {ETH Zurich, Zurich, Switzerland},
year = {2016}
}