Scalable Computational Methods for Large-Scale Stochastic Optimization under High-Dimensional Uncertainty

高维不确定性下大规模随机优化的可扩展计算方法

• 批准号: 2245674
• 负责人: Peng Chen
• 金额: $ 31万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2245674&HistoricalAwards=false
• 关键词: Scalable; Computational; Methods; Large; Scale

Large-scale simulation in computational science and engineering is often carried out not only to obtain insight about a system, but also as a basis for decision-making. When the decision variables represent the design or control of an engineered or natural system, and the system is governed by partial differential equations (PDEs) with uncertain input due to lack of knowledge or intrinsic variability, the task of determining the optimal design or control leads to a PDE-constrained stochastic optimization problem. Such problems abound across all areas of science and engineering. Examples include optimal control of subsurface flows, plasma fusion reactors, and chemical and materials processes; optimal structural design of aerospace, automotive, and civil infrastructure systems; and shape, layout, or topology optimization of biomedical, electronic, and nano-structured devices. There are several critical challenges in solving such problems including high dimensionality stemming from uncertainty and/or optimization variable spaces, and the need to solve large-scale PDEs with numerous samples of the uncertain parameters. This project will develop, analyze, and implement scalable computational methods to make tractable the solution of large-scale PDE-constrained stochastic optimization problems under high-dimensional uncertainty. These methods will be applied to subsurface flow problems with societal impact; software will be developed and disseminated widely in open source form. Graduate students will be involved and will receive interdisciplinary training. This project exploits the intrinsic structure of the stochastic optimization problems--in particular the intrinsic low dimensionality, smoothness, and geometry of the random parameter-to-objective map. Specifically, the components of the research include: (1) Analysis of the rank or spectrum decay of the Hessian of this map to prove intrinsic low-dimensionality for several classical stochastic PDE-constrained optimization problems. (2) Extension of local quadratic approximation-based stochastic optimization to that based on approximation of the Hessian as a translation invariant operator, higher order Taylor approximation, and multi-point Taylor approximation with mixture models. (3) Application to a specific large-scale and challenging problem of optimal flow control in a subsurface porous medium with a random permeability field. The methods developed in this project will apply to a wide class of PDE-constrained stochastic optimization problems. To make the methods accessible to broader communities and allow stochastic optimization specialists to prototype new algorithms and quickly run experiments, a Python library, SOUPy (Stochastic Optimization under high-dimensional Uncertainty in Python), will be implemented and released. Users will be able to rapidly prototype new PDE models and objective functions, as well as quickly implement new algorithms, conduct numerical experiments, and solve challenging problems in new domains in SOUPy.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

计算科学和工程中的大规模模拟通常不仅是为了获得有关系统的见解，而且是作为决策的基础。当决策变量代表工程或自然系统的设计或控制时，由于缺乏知识或内在的可变性，该系统受偏微分方程（PDE）的影响，确定最佳设计或控制的任务导致PDE构成的随机官方优化问题。这些问题在科学和工程的所有领域中都充满。例如，最佳控制地下流，等离子融合反应堆以及化学和材料过程；航空航天，汽车和民用基础设施系统的最佳结构设计；以及生物医学，电子和纳米结构设备的形状，布局或拓扑优化。在解决此类问题方面存在一些关键挑战，包括来自不确定性和/或优化变量空间的高维度，以及使用大量不确定参数的样本求解大规模PDE的需要。该项目将开发，分析和实施可扩展的计算方法，以使在高维不确定度下的大规模PDE受限随机优化问题的解决方案。这些方法将应用于与社会影响的地下流问题。软件将以开源形式开发和广泛传播。研究生将参与其中，并将接受跨学科培训。该项目利用了随机优化问题的内在结构，尤其是在内在的低维度，平滑度和随机参数对目标图的几何形状。具体而言，研究的组成部分包括：（1）该地图的Hessian的等级或频谱衰减的分析，以证明几种经典的随机PDE PDE构成的优化问题是内在的低维度。 （2）基于Hessian作为翻译不变的操作员的近似，高阶Taylor近似以及与混合模型的多点Taylor近似，将基于二次近似的随机优化扩展到了。 （3）应用于具有随机渗透率场的地下多孔介质中最佳流量控制的特定大规模和具有挑战性的问题。该项目中开发的方法将适用于一类PDE受限的随机优化问题。为了使更广泛的社区可以访问这些方法，并允许随机优化专家来原型新算法，并迅速运行实验，将实施和释放和释放这些方法，即python库（在Python的高维不确定性下的随机优化）。用户将能够快速原型新的PDE模型和目标功能，并迅速实施新的算法，进行数值实验，并解决SOUPY中新领域中具有挑战性的问题。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力功能和广泛的影响来评估CRETERIA的评估，这是值得通过评估的支持。

项目成果

An Offline-Online Decomposition Method for Efficient Linear Bayesian Goal-Oriented Optimal Experimental Design: Application to Optimal Sensor Placement

高效线性贝叶斯目标导向最优实验设计的离线在线分解方法：在最优传感器放置中的应用

• DOI: 10.1137/21m1466542
• 发表时间: 2023
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Wu, Keyi;Chen, Peng;Ghattas, Omar
• 通讯作者: Ghattas, Omar

Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network

• DOI: 10.1007/s10915-023-02145-1
• 发表时间: 2022-01
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Keyi Wu;Thomas O'Leary-Roseberry;Peng Chen;O. Ghattas

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

• DOI: 10.1016/j.jcp.2023.112101
• 发表时间: 2023-04-12
• 期刊: JOURNAL OF COMPUTATIONAL PHYSICS
• 影响因子: 4.1
• 作者: Luo，Dingcheng;Cao，Lianghao;Oden，Tinsley
• 通讯作者: Oden，Tinsley

A Fast and Scalable Computational Framework for Large-Scale High-Dimensional Bayesian Optimal Experimental Design

用于大规模高维贝叶斯最优实验设计的快速且可扩展的计算框架

• DOI: 10.1137/21m1466499
• 发表时间: 2023
• 期刊: SIAM/ASA Journal on Uncertainty Quantification
• 作者: Wu, Keyi;Chen, Peng;Ghattas, Omar
• 通讯作者: Ghattas, Omar