Scalable Algorithms for Uncertainty Quantification and Bayesian Inference with Applications to Computational Mechanics

不确定性量化和贝叶斯推理的可扩展算法及其在计算力学中的应用

• 批准号: RGPIN-2017-06375
• 负责人: Sarkar, Abhijit
• 金额: $ 2.04万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=749108
• 关键词: Scalable; Algorithms; Uncertainty; Quantification; Bayesian

The proposed statistical framework intends to provide a rational approach to reconciling running computational simulations with measurement data in uncertain and rapidly changing environments for accurate and realistic numerical predictions for informed and optimal decision-making. The long-term objective of the proposed research is to develope uncertainty quantification, data assimilation and model selection algorithms which can exploit the extreme-scale parallelism required to effectively leverage petascale and future exascale systems with millions of cores and accelerators (e.g. graphics processing units and coprocessors). The proposed algorithms will be applied to tackle computational stochastic mechanics problems related to (a) real-time nonlinear aeroelastic computations using streaming wind-tunnel data; (b) uncertainty quantification in middle frequency structural dynamics; and (c) nonlinear (elasto-plastic) seismic wave propagations through random geological media. The novelties of the proposed research are: (1) the mathematical formulation and distributed implemention of MH-MCMC algorithms for Bayesian parameter estimation and model selection in conjunction with its experimental validation for nonlinear aeroelastic computation using streaming wind-tunnel data; and (2) the development of an intrusive polynomial chaos-based multi-level domain decomposition algorithm for SPDES for ultra-scale computations in petascale/future exascale systems, along with its applications to the middle frequency structural dynamics and elasto-plastic seismic wave propagation in random soil strata. The uncertainty quantification and data assimilation in computational models will boost public confidence and regulatory acceptance in order to assess the safety and reliability of engineering systems for aeroelastic performance of long-span bridges, air vehicles, seismic risk assessment of dams and nuclear reactors and, detection of military activities from seismic signatures. The proposed Bayesian estimation framework for computional modeling can bridge the gap between experimentalists and numerical modelers in various disciplines in science and engineering. Capitalizing on the investments in large-scale national computing facilities, the proposed research initiatives will offer technological leadership to Canada including the development of a highly skilled workforce capable of high performance computing, uncertainty quantification and statistical inference relevant to computational and data science applications.

所提出的统计框架旨在提供一种合理的方法来协调不确定和快速变化的环境中运行的计算模拟与测量数据，以便做出准确和现实的数值预测，从而做出明智的最佳决策。拟议研究的长期目标是开发不确定性量化、数据同化和模型选择算法，这些算法可以利用有效利用具有数百万个核心和加速器（例如图形处理单元和协处理器）的千万亿级和未来百亿亿级系统所需的极端规模并行性。所提出的算法将用于解决与以下相关的计算随机力学问题：（a）使用流风洞数据进行实时非线性气动弹性计算； (b) 中频结构动力学的不确定性量化； (c) 通过随机地质介质的非线性（弹塑性）地震波传播。本研究的新颖之处在于：（1）用于贝叶斯参数估计和模型选择的 MH-MCMC 算法的数学公式和分布式实现，以及使用流风洞数据进行非线性气动弹性计算的实验验证； (2) 开发一种基于侵入多项式混沌的 SPDES 多级域分解算法，用于千万亿级/未来百亿亿级系统的超尺度计算，及其在随机土层中的中频结构动力学和弹塑性地震波传播中的应用。计算模型中的不确定性量化和数据同化将增强公众信心和监管接受度，以评估大跨桥梁、飞行器的气动弹性性能、大坝和核反应堆的地震风险评估以及根据地震特征检测军事活动的工程系统的安全性和可靠性。所提出的计算建模贝叶斯估计框架可以弥合科学和工程各个学科的实验学家和数值建模者之间的差距。利用对大型国家计算设施的投资，拟议的研究计划将为加拿大提供技术领先地位，包括培养能够进行高性能计算、不确定性量化和与计算和数据科学应用相关的统计推断的高技能劳动力。