Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications
Stochastic Collocation With Non-Gaussian Correlated Process Variations: Theory, Algorithms, and Applications
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DOI：
10.1109/tcpmt.2018.2889266
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Chunfeng Cui;Zheng Zhang
中科院分区：
文献类型：
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作者：
Chunfeng Cui;Zheng Zhang
随机谱方法已经在许多工程问题的不确定性量化方面取得了巨大的成功，包括变化感知的电子和光子设计自动化。最先进的技术使用广义多项式混沌展开，并假设所有随机参数是独立的或高斯相关的。这一假设在实际应用中很少是正确的。如何处理非高斯相关的随机参数是一个长期而根本的挑战：如何在相关的不确定参数空间中选择基函数和执行投影步骤尚不清楚。首先提出了一组新的基函数来很好地捕捉非高斯相关参数的影响，然后提出了一种自动的基于优化的求积方法，在相关参数空间中利用少量的模拟样本进行基于投影的随机配置。我们进一步为我们提出的方法的复杂性和误差界提供了一些理论证明。在几个合成集成电路、电子集成电路和光子集成电路上的数值实验表明，该方法具有接近指数收敛的速度，并且比蒙特卡罗方法有显著的加速(700-6000倍)。在此基础上，可以进一步解决其他许多具有非高斯相关不确定性的公开问题。
Stochastic spectral methods have achieved a great success in the uncertainty quantification of many engineering problems, including variation-aware electronic and photonic design automation. State-of-the-art techniques employ generalized polynomial-chaos expansions and assume that all random parameters are independent or Gaussian correlated. This assumption is rarely true in real applications. How to handle non-Gaussian correlated random parameters is a long-standing and fundamental challenge: It is not clear how to choose basis functions and to perform a projection step in a correlated uncertain parameter space. This paper first presents a new set of basis functions to well capture the impact of non-Gaussian correlated parameters and then proposes an automatic and optimization-based quadrature method to perform projection-based stochastic collocation with a few simulation samples in the correlated parameter space. We further provide some theoretical proofs for the complexity and error bound of our proposed method. The numerical experiments on several synthetic, electronic, and photonic integrated circuit examples show the nearly exponential convergence rate of our approach and its significant ( $700 \times $ – $6000 \times $ ) speedup than Monte Carlo. Many other open problems with non-Gaussian correlated uncertainties can be further solved based on this paper.