Optimization of PDEs with Uncertain Inputs
Optimization of PDEs with Uncertain Inputs
复制标题
具有不确定输入的偏微分方程优化
DOI：
10.1007/978-1-4939-8636-1_2
复制
发表时间：
2018
期刊：
影响因子：
3
通讯作者：
A. Shapiro
中科院分区：
文献类型：
--
作者：
D. Kouri;A. Shapiro
不确定性几乎遍及所有的科学和工程应用，包括由偏微分方程（PDEs）控制的系统的最优控制和设计。在许多应用中，确定对未知边界条件、不准确系数和无法验证的建模假设的固有不确定性具有弹性的最佳解决方案至关重要。在本教程中，我们开发了PDE约束优化问题的一般理论，其中PDE的输入或系数是不确定的。我们讨论了许多将风险偏好和保守性纳入优化问题公式的方法，这些方法受到具体工程应用的激励。最后讨论了非侵入式求解方法和数值算例。
Uncertainty pervades nearly all science and engineering applications including the optimal control and design of systems governed by partial differential equations (PDEs). In many applications, it is critical to determine optimal solutions that are resilient to the inherent uncertainty in unknown boundary conditions, inaccurate coefficients, and unverifiable modeling assumptions. In this tutorial, we develop a general theory for PDE-constrained optimization problems in which inputs or coefficients of the PDE are uncertain. We discuss numerous approaches for incorporating risk preference and conservativeness into the optimization problem formulation, motivated by concrete engineering applications. We conclude with a discussion of nonintrusive solution methods and numerical examples.