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

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和测量数据，以便为知情和最佳决策提供准确和现实的数值预测。所提议的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，这些算法可以利用极端规模的并行性，有效地利用千兆级和未来的百亿亿级系统所需的数百万核和加速器（例如图形处理单元和协处理器）。所提出的算法将应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)非线性（弹塑性）地震波在随机地质介质中的传播。本文研究的新颖之处有：(1)提出了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，并结合流风洞数据进行了非线性气动弹性计算的实验验证；(2)开发了一种基于干扰多项式混沌的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，并将其应用于随机土层中频结构动力学和弹塑性地震波传播。计算模型中的不确定性量化和数据同化将提高公众信心和监管接受度，以便评估大跨度桥梁、飞行器、大坝和核反应堆的气动弹性性能的工程系统的安全性和可靠性，以及从地震特征中探测军事活动。所提出的计算建模贝叶斯估计框架可以在科学和工程的各个学科的实验和数值建模之间架起一座桥梁。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，包括发展具有高性能计算能力的高技能劳动力，与计算和数据科学应用相关的不确定性量化和统计推断。

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.