A Hybrid Polynomial Chaos Expansion and Gaussian Process Regression Method for Forward Uncertainty Quantification of Integrated Circuits

This paper introduces a novel kernel-based formulation for the efficient uncertainty quantification of integrated circuits. The method combines the polynomial chaos expansion (PCE) and Gaussian process regression (GPR) frameworks, the former to provide closed-form statistical information and the latter for an efficient training. In essence, the PCE coefficients are computed using a suitable Bayesian formulation that involves the definition of a special implicit kernel based on an infinite sequence of Hermite polynomials. The proposed method is illustrated based on a network with microstrip lines.