Conservative Surrogate Modeling of Crosstalk with Application to Uncertainty Quantification

Machine learning methods are attracting a great interest as surrogate modeling tools for signal and power integrity problems. However, an open issue is that it is often difficult to assess the model trustworthiness in generalizing beyond the training data. In this regard, Gaussian process (GP) models notably provide an indication of the prediction confidence due to the limited amount of training samples. They are wildly used as surrogates in design exploration, optimization, and uncertainty quantification tasks. Nevertheless, their prediction confidence does not account for the uncertainty introduced by the estimation of the GP parameters, which is also part of the training process. In this paper, we discuss two improved GP formulations that take into account the additional uncertainty related to the estimation of (some) GP parameters, thereby leading to more reliable and conservative confidence levels. The proposed framework is applied to the uncertainty quantification of the maximum transient crosstalk in a microstrip interconnect.