Gradient-Enhanced Polynomial Chaos Methods for Circuit Simulation

Abstract

Uncertainty Quantification (UQ) is an important and emerging topic in electronic design automation (EDA), as parametric uncertainties are a significant concern for the design of integrated circuits. Historically, various sampling methods such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) have been employed, but these methods can be prohibitively expensive. Polynomial Chaos Expansion (PCE) methods are often proposed as an alternative to sampling. PCE methods have a number of variations, representing tradeoffs. Regression-based PCE methods, for example, can be applied to existing sample sets and don’t require specific quadrature points. However, this comes at the cost of accuracy. In this paper we explore the idea of enhancing regression-based PCE methods using gradient information. The gradient information is provided by an intrusive adjoint sensitivity algorithm embedded in the circuit simulator.