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

拟议的统计框架旨在提供一种合理的方法，在不确定和快速变化的环境中协调运行的计算模拟与测量数据，以便为知情和最优决策提供准确和现实的数字预测。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千万亿级和未来亿级级系统所需的极端规模并行性，这些系统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)。所提出的算法将用于解决与以下问题有关的计算随机力学问题：(A)使用流动风洞数据进行实时非线性气动弹性计算；(B)中频结构动力学中的不确定性量化；以及(C)非线性(弹塑性)地震波在随机地质介质中的传播。本文的创新之处在于：(1)建立了贝叶斯参数估计和模型选择的MH-MCMC算法的数学模型和分布式实现方法，并利用流动风洞数据进行了非线性气动弹性计算的实验验证；(2)发展了一种侵入式多项式混沌多层区域分解算法，用于PETSCALE/未来亿级系统超大规模计算的SPDES，及其在中频结构动力学和随机土层中的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提高公众信心和监管接受度，以便评估大跨度桥梁、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从地震信号检测军事活动的工程系统的安全性和可靠性。提出的用于计算建模的贝叶斯估计框架可以在科学和工程的不同学科中弥合实验者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，拟议的研究倡议将为加拿大提供技术领先，包括发展一支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理的高技能劳动力队伍。

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.