Conservative Gaussian Process Models for Uncertainty Quantification and Bayesian Optimization in Signal Integrity Applications

Surrogate modeling is being increasingly adopted in signal and power integrity analysis to assist design exploration, optimization, and uncertainty quantification tasks. In this scenario, machine learning methods are attracting an ever-growing interest over alternative and well-consolidated techniques due to their data-driven nature. However, an open issue is to properly assess the trustworthiness of predictions when generalizing beyond training data. Among various machine learning tools, Gaussian process regression (GPR) has the notable feature of providing an estimate of the prediction uncertainty (or confidence) due to the lack of data. Nevertheless, the uncertainty introduced by the estimation of the Gaussian process parameters, which is part of the training process, is typically not accounted for. In this paper, we introduce improved GPR formulations that take into account the additional uncertainty related to the estimation of (some of) the Gaussian process parameters, thereby providing a more accurate estimate of the actual prediction confidence. Furthermore, the advocated framework is extended to uncertainty quantification and Bayesian optimization settings. The technique is applied to two test cases concerning the analysis of crosstalk in a transmission line network and of the frequency-domain response of a microstrip line with a ground plane discontinuity.