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

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.