Stochastic behavioral modeling of analog/mixed-signal circuits by maximizing entropy

Maximum entropy (MAXENT) is a powerful and flexible method for estimating the arbitrary probabilistic distribution of a stochastic variable with moment constraints. However, modeling the stochastic behavior of analog/mixed-signal (AMS) circuits using MAXENT is still unknown. In this paper, we present a MAXENT based approach to efficiently model the arbitrary behavioral distribution of AMS circuits with high accuracy. The exact behavioral distribution can be approximated by a product of exponential functions with different Lagrangian multipliers. The closest approximation can be obtained by maximizing Shannon's information entropy subject to moment constraints, leading to a nonlinear system. Classic Newton's method is used to solve the nonlinear system for the Lagrangian multipliers, which can further recover the arbitrary behavioral distribution of AMS circuits. Extensive experiments on different circuits demonstrate that the proposed MAXENT based approach offers better stability and improves the accuracy up to 110% when compared to previous AWE-based moment matching approaches, and offers up to 592x speedup when compared to Monte Carlo method.