Probabilistic Uncertainty Quantification of Microwave Circuits Using Gaussian Processes

In this article, a probabilistic machine learning framework based on Gaussian process regression (GPR) and principal component analysis (PCA) is proposed for the uncertainty quantification (UQ) of microwave circuits. As opposed to most surrogate modeling techniques, GPR models inherently carry information on the model prediction uncertainty due to unseen data. This article shows how the inherent uncertainty of GPR pointwise predictions can be combined with the uncertainty of the design parameters to provide global statistical information on the device performance with the inclusion of confidence bounds. The model confidence is possibly improved by increasing the amount of training data. In addition, PCA is employed to effectively deal with problems with multiple and possibly complex-valued output components, such as those involving the UQ of time-domain responses or multiport scattering parameters. The proposed technique is successfully applied to two low-noise amplifier designs subject to the process variation of up to 25 parameters. Comparisons against the state-of-the-art polynomial chaos expansion method demonstrates that GPR achieves superior accuracy, while additionally providing information on the prediction confidence.