Citation: De Witte, D.; Qing, J.;
Couckuyt, I.; Dhaene, T.; Vande
Ginste, D.; Spina, D. A Robust
Bayesian Optimization Framework
for Microwave Circuit Design under
Uncertainty. Electronics 2022, 11, 2267.
https://doi.org/10.3390/
electronics11142267
Academic Editors: Phivos Mylonas,
Katia Lida Kermanidis and Manolis
Maragoudakis
Received: 17 June 2022
Accepted: 18 July 2022
Published: 20 July 2022
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Article
A Robust Bayesian Optimization Framework for Microwave
Circuit Design under Uncertainty
Duygu De Witte * , Jixiang Qing , Ivo Couckuyt , Tom Dhaene , Dries Vande Ginste
and Domenico Spina
IDLab, Department of Information Technology, Ghent University-imec, Technologiepark-Zwijnaarde 126,
9052 Ghent, Belgium; jixiang.qing@ugent.be (J.Q.); ivo.couckuyt@ugent.be (I.C.); tom.dhaene@ugent.be (T.D.);
dries.vandeginste@ugent.be (D.V.G.); domenico.spina@ugent.be (D.S.)
* Correspondence: duygu.kan@ugent.be
Abstract:
In modern electronics, there are many inevitable uncertainties and variations of design
parameters that have a profound effect on the performance of a device. These are, among others,
induced by manufacturing tolerances, assembling inaccuracies, material diversities, machining
errors, etc. This prompts wide interests in enhanced optimization algorithms that take the effect of
these uncertainty sources into account and that are able to find robust designs, i.e., designs that are
insensitive to the uncertainties early in the design cycle. In this work, a novel machine learning-based
optimization framework that accounts for uncertainty of the design parameters is presented. This
is achieved by using a modified version of the expected improvement criterion. Moreover, a data-
efficient Bayesian Optimization framework is leveraged to limit the number of simulations required
to find a robust design solution. Two suitable application examples validate that the robustness is
significantly improved compared to standard design methods.
Keywords: Bayesian Optimization; robust optimization; Gaussian processes; microwave design
1. Introduction
The emergence of new technologies and the constant miniaturization of integrated
circuits challenge engineers to obtain designs that satisfy stringent functional specifications
and signal integrity (SI) requirements, as well as electromagnetic compatibility (EMC) con-
straints. Various optimization techniques are used to find optimal designs and improve the
device performance at the early design stage [
1
–
3
]. While in other engineering domains it
is sometimes possible to solve complex numerical equations with efficient-stable numerical
methods [
4
–
6
]; given the high computational cost of simulating modern high-frequency
circuits, surrogate modeling techniques are typically utilized to efficiently perform design
optimization [
7
–
11
]. In particular, since the complexity of design optimization problems is
constantly increasing, machine learning-based algorithms have become a popular choice to
cope with the multiscale issues in radio frequency (RF) and microwave designs [12–15].
While, theoretically speaking, the performance of an electromagnetic device can be
improved by applying adequate optimization techniques, in reality, there are many un-
avoidable geometrical and material uncertainties that degrade the device’s performance.
In particular, the real-life performance of a device is significantly affected by the manu-
facturing technology employed, the assembling inaccuracy, uncertainties due to material
diversities, operation environment, etc. From the perspective of industrial design and
manufacturing, there are two types of optimization models: deterministic and robust
optimization models [
16
]. In deterministic optimization methods, all design parameters
and system variables assume known values, which are freely specified by designers. Since
no random variability and data uncertainty are investigated, deterministic optimization
models fall short to find robust designs. In contrast, the latter are considered (to a certain
extent) insensitive to variations of design parameters.
Electronics 2022, 11, 2267. https://doi.org/10.3390/electronics11142267 https://www.mdpi.com/journal/electronics
