具有非高斯相关过程变化的随机格点：理论、算法与应用
Stochastic Collocation with Non-Gaussian Correlated Process Variations: Theory, Algorithms and Applications
AI总结：
本文提出了一种基于优化的方法，用于自动确定随机格点投影步骤所需的求积节点和权重，开发了高效的随机格点算法，用于处理非高斯相关参数的系统，并提供了理论证明和数值实验，展示了近指数收敛率和优异的效率。
摘要：
随机谱方法在许多工程问题的不确定性量化中取得了巨大成功，包括受制造过程变化影响的电子和光子集成电路。现有技术使用广义多项式-混沌展开，并几乎总是假设所有随机参数相互独立或高斯相关。然而，这一假设在实际应用中很少成立。如何处理非高斯相关随机参数是一个长期存在的根本性挑战。主要瓶颈是缺乏理论和计算方法，用于在相关不确定参数空间中执行投影步骤。本文提出了一种基于优化的方法，以自动确定投影步骤所需的求积节点和权重，并开发了用于非高斯相关参数系统的高效随机格点算法。我们还为所提出方法的复杂性和误差界提供了理论证明。在合成、电子和光子集成电路示例上的数值实验展示了所提出方法的近指数收敛率和优异的效率。许多其他具有挑战性的不确定性相关问题都可以基于这项工作进一步解决。
英文摘要：
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques employ a generalized polynomial-chaos expansion, and they almost always assume that all random parameters are mutually independent or Gaussian correlated. However, this assumption is rarely true in real applications. How to handle non-Gaussian correlated random parameters is a long-standing and fundamental challenge. A main bottleneck is the lack of theory and computational methods to perform a projection step in a correlated uncertain parameter space. This paper presents an optimization-based approach to automatically determinate the quadrature nodes and weights required in a projection step, and develops an efficient stochastic collocation algorithm for systems with non-Gaussian correlated parameters. We also provide some theoretical proofs for the complexity and error bound of our proposed method. Numerical experiments on synthetic, electronic and photonic integrated circuit examples show the nearly exponential convergence rate and excellent efficiency of our proposed approach. Many other challenging uncertainty-related problems can be further solved based on this work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
