Sparse Linear Regression (SPLINER) Approach for Efficient Multidimensional Uncertainty Quantification of High-Speed Circuits

Abstract

This paper presents a novel linear regression-based polynomial chaos (PC) approach for the efficient multidimensional uncertainty quantification of general distributed and lumped high-speed circuit networks. The key feature of this paper is the development of a modified Fedorov search algorithm based on the D -optimal criterion that expeditiously locates a highly sparse set of nodes within the multidimensional random space where the original network needs to be probed. Specifically, the number of selected nodes is kept equal to the number of unknown PC coefficients of the network response, thereby making this approach substantially more efficient than the conventional linear regression approach which is based on an oversampling methodology. Additionally, due to the D -optimal criterion, this approach ensures highly accurate recovery of the PC coefficients. The validity of this paper is established through multiple numerical examples.