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

R. Krishnan, Wei Wu, Fang Gong, Lei He
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引用次数: 11

Abstract

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.
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基于熵最大化的模拟/混合信号电路随机行为建模
最大熵(MAXENT)是一种强大而灵活的方法,用于估计具有矩约束的随机变量的任意概率分布。然而,利用MAXENT建模模拟/混合信号(AMS)电路的随机行为仍然是未知的。在本文中,我们提出了一种基于MAXENT的方法来高效、高精度地模拟AMS电路的任意行为分布。精确的行为分布可以用不同拉格朗日乘子的指数函数的乘积来近似。在矩约束下,通过最大化香农信息熵来获得最接近的近似,从而得到非线性系统。采用经典牛顿法求解拉格朗日乘法器的非线性系统,可以进一步恢复AMS电路的任意行为分布。在不同电路上进行的大量实验表明,与之前基于awe的矩匹配方法相比,基于MAXENT的方法具有更好的稳定性,精度提高了110%,与蒙特卡罗方法相比,速度提高了592x。
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