Uncertainty Quantification and Sensitivity Analysis of Crosstalk in PCB Lines via the Combination of Machine Learning and Polynomial Chaos Expansion

Manufacturing tolerances are becoming one of the major limitations to achieving high data rates in modern integrated circuits. Polynomial chaos expansion (PCE) recently became a popular alternative to classical Monte Carlo for efficient uncertainty quantification (UQ). Statistical moments and sensitivity information are analytically derived from the PCE coefficients. However, computing the model coefficients typically requires a large amount of data samples from possibly expensive design simulations. On the other hand, kernel-based machine learning methods were recently employed to create efficient surrogate models with a limited amount of training data. In this paper, we combine the kernel Gaussian process regression (GPR) method and the PCE. The former is used to surrogate the expensive simulator in the calculation of PCE coefficients via numerical integration. The use of GPR also allows obtaining confidence levels of the estimated PCE coefficients and the relative statistical information. The proposed hybrid PCE-GPR method is applied to UQ of maximum crosstalk in a PCB interconnect, for which higher accuracy with a very limited amount of data is obtained compared to state-of-the-art approaches.