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

这一学院早期职业发展(CALEAR)计划研究项目将为设计、分析和实施不确定性量化的统计方法创建一个系统框架，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政策制定和许多行业的绩效评估、风险分析和决策任务中。由于高保真模拟模型的计算负担沉重，随机问题的内在高维性，以及数据-系统集成的结构复杂性，最近工业系统复杂性的扩大对使用传统统计方法来同化数据提出了挑战。该研究计划将计算模拟与非参数统计和现代优化工具的使用相结合，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模拟工具，用于评估自动化车辆的安全性。这些工具将通过机构协作网络和在线公共渠道分发给相关的政府和工业单位。这项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，开发一门新的跨学科研究生课程，并提供关于工程专业社会角色的实践案例研究。该教育计划还将为研究生提供培训，并创造本科生的研究机会，特别是在工程和数据科学方面。具体的研究目标将在随机和模拟分析中的四个基本问题上开发统计不确定性量化方法：1)罕见事件预测和计算；2)模拟分析中输入模型误差的传播；3)从输出数据校准随机输入模型；以及4)量化和丰富数据驱动的随机优化中所获得的解的可行性。每个问题都提出了不同的挑战，这些挑战来自于小样本偏差、巨大的计算负担、高维度或阻碍现有方法有效性的过度保守。这项研究将强调一个统一的框架，以使用新的公式和对随机空间上的优化程序的分析来生成性能估计，并通过非参数统计方法得出或证明约束。这项研究将包括开发置信限和量化对模型错误指定的稳健性，以及确保在优化和模拟效率方面的计算可处理性的算法分析。开发的技术将在蒙特卡洛模拟、随机和稳健优化以及统计等领域进行交叉施肥。研究成果还将使下一代工程师在使用有利于他们未来职业生涯的计算和统计工具方面具有多方面的视角。

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.