Uncertainty Quantification for Complex Computer Models

不确定性量化是一门现代交叉学科，它综合了统计学、数值分析和计算应用数学中的方法论，以表征计算机模型中固有的不确定性。由于计算能力、逼真的物理模型和高效的数值方法的快速发展，计算机模型现在被广泛地用于描述复杂系统。这样的模型被用作研究系统的物理实验的更快和更低成本的替代方案。复杂计算机模型的UQ有助于产生更准确的预测，因此对于航空航天、可再生能源、气候建模和制造等许多领域的风险评估和决策至关重要。例如，汽车工程师使用计算机模型来设计新的、更安全的车辆，速度更快，成本更低，而不必一次又一次地撞毁实际车辆。UQ方法，如设计优化、模型偏差量化、模型验证和验证、代理建模等，被认为是提高汽车质量和可靠性的关键。随着计算机模型的数据量和维度的增加，从计算机模型分析数据的计算成本可能会高得令人望而却步。随着计算机模型的复杂性增加，现有的方法可能不适用于建立准确的替代模型，从而阻止了进一步的统计推断，如模型校准、优化、灵敏度分析和反问题。拟议的研究计划旨在通过在实验设计、替代模型、模型校准、反问题和复杂计算机模型的降维方面开发新的统计理论和方法来解决这些关键挑战。拟议的研究集中于以下三个主题：(A)动态计算机模型的大规模逆问题、功能校准和实验设计；(B)具有多变量定性响应、混合响应和删失响应的计算机模型的代理建模、逆问题和实验设计；以及(C)大规模多保真计算机模型的仿真、多保真计算机模型的设计和降维。预期的研究结果将极大地促进复杂计算机模型中UQ统计方法的技术水平。新的方法论将被纳入R等公开发布的软件中，因此直接使研究人员和从业者受益。该项目还将创造和整合教育机会，包括让本科生接触复杂的计算机模型中的UQ，为研究生提供应用方法论所需的高级技能，以及指导博士生成为UQ统计研究的领导者。

Uncertainty quantification (UQ) is a modern inter-disciplinary science that integrates methodologies in statistics, numerical analysis and computational applied mathematics to characterize the uncertainties inherent in computer models. Due to rapid advances in computing power, realistic physical modelling and efficient numerical methods, computer models are now widely used to describe complex systems. Such models are used as a faster and less costly alternative to physical experimentation to study systems. UQ for complex computer models helps to produce more accurate predictions and thus is critical for risk assessment and decision making in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. For example, automotive engineers use computer models to design new, safer vehicles much more quickly, and cheaply without having to crash actual cars over and over. UQ methods, such as design optimization, model bias quantification, model verification and validation, and surrogate modeling, are deemed essential in improving the quality and reliability of automotive. As data size and dimensions of computer models increase, the computational cost for analyzing data from computer models can be prohibitively expensive. With the increasing complexity of computer models, the existing methodology may not be applicable to build accurate surrogate models, thereby preventing further statistical inference such as model calibration, optimization, sensitivity analysis and inverse problem. The proposed research program aims to address these critical challenges by developing novel statistical theory and methodologies on experimental design, surrogate modelling, model calibration, inverse problems, and dimension reduction for complex computer models. The proposed research focuses on the following three themes: (a) large-scale inverse problems, functional calibration and design of experiments for dynamic computer models; (b) surrogate modelling, inverse problems, and design of experiments for computer models with multivariate qualitative responses, mixed responses; and censored responses; and (c) emulation of large-scale multi-fidelity computer models, design and dimension reduction of multi-fidelity computer models. The expected research outcomes will significantly advance the current state of the art of statistical approaches for UQ in complex computer models. The new methodologies will be incorporated into publicly released software such as R, therefore directly benefiting researchers and practitioners. The project will also create and integrate educational opportunities, including exposing undergraduate students to UQ in complex computer models, providing graduate students the advanced skills needed to apply the methodologies, and mentoring Ph.D students to become leaders in UQ statistical research.