Anisotropic formulation of hyperbolic polynomial chaos expansion for high-dimensional variability analysis of nonlinear circuits

In this paper, a new polynomial chaos (PC) approach for the fast variability analysis of high speed nonlinear circuits is presented. The key feature of this work is the development of an alternative anisotropic hyperbolic scheme to intelligently truncate general PC expansions. This truncation scheme not only prunes the statistically insignificant bases arising from the high degree interactions of the random dimensions but also modulates the maximum degree of expansion along each dimension based on the contribution of that dimension to the response surface. The proposed approach results in a substantially sparser PC expansion for marginal loss of accuracy.