CAREER: Optimization-based Quantification of Statistical Uncertainty in Stochastic and Simulation Analysis

该学院早期职业发展（Career）计划研究项目将创建一个系统框架，用于设计、分析和实施不确定性量化的统计方法，有效地将数据整合到随机和模拟分析中。这些分析经常出现在绩效评估、风险分析和政策制定和许多行业的决策任务中。由于高保真仿真模型的沉重计算负担、随机问题固有的高维性以及数据系统集成的结构复杂性，近年来工业系统复杂性的扩大对传统统计方法在同化数据方面的使用提出了挑战。该研究计划将混合使用计算模拟与非参数统计和现代优化工具，以产生既统计准确又计算高效的方法。如果成功，研究成果将有助于开发基于数据驱动的仿真工具，用于评估自动驾驶汽车的安全性。这些工具将通过机构协作网络和在线公共渠道分发给有关的政府和工业单位。该研究还将提供可靠的、数据驱动的方法来评估风险，并校准对国内经济至关重要的各个行业使用的模拟平台。该教育计划将扩展本科模拟课程，开发新的跨学科研究生课程，并提供有关工程专业社会角色的实际案例研究。该教育项目还将为研究生提供培训，并为本科生创造研究机会，特别是为工程和数据科学领域代表性不足的少数族裔提供培训。具体研究目标是在随机分析和模拟分析的四个基本问题中发展统计不确定性量化方法：1)罕见事件预测和计算；2)仿真分析中输入模型误差的传播；3)根据输出数据标定随机输入模型；4)量化和丰富数据驱动随机优化解的可行性。每个问题都提出了不同的挑战，这些挑战来自小样本偏差、巨大的计算负担、高维数或阻碍现有方法有效性的过度保守性。该研究将强调一个统一的框架，使用新的公式和分析随机空间上的优化程序来生成性能估计，并通过非参数统计方法推导或证明约束。研究将包括置信界限的发展和模型错误规范的稳健性量化，以及算法分析，以确保在优化和模拟效率方面的计算可追溯性。所开发的技术将在蒙特卡洛模拟，随机和鲁棒优化以及统计等领域交叉施肥。研究成果还将使下一代工程师在使用计算和统计工具方面具备多方面的视角，这将有利于他们未来的职业生涯。

This Faculty Early Career Development (CAREER) Program research project will create a systematic framework for designing, analyzing, and implementing statistical methods for uncertainty quantification that effectively integrate data into stochastic and simulation analyses. These analyses arise routinely in performance evaluations, risk analytics, and decision-making tasks in policymaking and many industries. The recent expansion of industrial system complexities challenges the use of conventional statistical methods in assimilating data, due to the heavy computational burden of high-fidelity simulation models, the intrinsic high dimensionality of stochastic problems, and the structural complications of data-system integration. The research program will blend the use of computational simulation with nonparametric statistics and modern optimization tools to produce methodologies that are both statistically accurate and computationally efficient. If successful, the research outcomes will aid in developing data-driven simulation-based tools for evaluating automated vehicle safety. The tools will be disseminated to relevant governmental and industrial units through institutional collaborative networks and online public channels. The research will also provide reliable, data-driven methodologies to assess risks and calibrate the simulation platforms used in various industries vital to the domestic economy. The education program will expand the undergraduate simulation curriculum, develop a new interdisciplinary graduate course, and provide practical case studies on the societal roles of the engineering profession. The education program will also provide training for graduate students and create undergraduate research opportunities, especially for under-represented minorities in engineering and data science.The specific research objectives will develop statistical uncertainty quantification methods in four fundamental problems in stochastic and simulation analyses: 1) Rare-event prediction and computation; 2) Propagation of input model errors in simulation analysis; 3) Calibration of stochastic input models from output data; and 4) Quantification and enrichment of the feasibility of obtained solutions in data-driven stochastic optimization. Each problem presents distinct challenges arising from small-sample bias, immense computational burden, high dimensionality, or over-conservativeness that impedes the effectiveness of existing methods. The research will emphasize a unified framework to generate performance estimates using new formulations and analyses of optimization programs posited over stochastic spaces, with constraints derived or justified via nonparametric statistical methods. The research will encompass the development of confidence bounds and the quantification of robustness to model misspecification, and the algorithmic analyses that ensure computational tractability in terms of optimization and simulation efficiencies. The techniques developed will cross-fertilize areas across Monte Carlo simulation, stochastic and robust optimization, and statistics. The research outcomes will also equip next-generation engineers with multi-faceted perspectives in using computational and statistical tools that will benefit their future careers.