Robust Adaptive Least Squares Polynomial Chaos Expansions in High-Frequency Applications

TL;DR

This paper introduces a robust, adaptive polynomial chaos expansion method for high-frequency electromagnetic models, utilizing sequential experimental design and sensitivity-based basis selection to improve approximation accuracy and robustness.

Contribution

It develops a novel adaptive least squares polynomial chaos algorithm with sequential design and sensitivity-driven basis construction for high-frequency electromagnetic applications.

Findings

Optimistic criteria yield higher average accuracy.

Strict criteria offer more robustness across designs.

Proposed criteria balance accuracy and robustness effectively.

Abstract

We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic high-frequency electromagnetic models in a black-box way, in particular, given only a dataset of random parameter realizations and the corresponding observations regarding a quantity of interest, typically a scattering parameter. The construction of the polynomial basis is based on a greedy, adaptive, sensitivity-related method. The sequential expansion of the experimental design employs different optimality criteria, with respect to the algebraic form of the least squares problem. We investigate how different conditions affect the robustness of the derived surrogate models, that is, how much the approximation accuracy varies given different experimental designs. It is found that relatively optimistic criteria perform on average better than stricter ones, yielding superior approximation accuracies for equal dataset sizes. However, the results of strict criteria are significantly more robust, as reduced variations regarding the approximation accuracy are obtained, over a range of experimental designs. Two criteria are proposed for a good accuracy-robustness trade-off.