Uncertainty Quantification for Complex Computer Models

复杂计算机模型的不确定性量化

• 批准号: RGPIN-2019-04725
• 负责人: Lin, Chunfang
• 金额: $ 1.46万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=677339
• 关键词: Uncertainty; Quantification; Complex; Computer; Models

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.**

不确定性量化（UQ）是一门综合了统计学、数值分析和计算应用数学方法来表征计算机模型固有不确定性的现代跨学科科学。由于计算能力的快速发展，逼真的物理建模和有效的数值方法，计算机模型现在被广泛用于描述复杂系统。这种模型被用作一种比物理实验更快、成本更低的方法来研究系统。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、气候建模和制造业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更快、更便宜地设计新的、更安全的车辆，而不必一次又一次地碰撞真正的汽车。UQ方法，如设计优化、模型偏差量化、模型验证和验证以及代理建模，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大小和尺寸的增加，分析计算机模型数据的计算成本可能会非常昂贵。随着计算机模型的日益复杂，现有的方法可能无法建立准确的代理模型，从而阻碍了模型校准、优化、灵敏度分析和逆问题等进一步的统计推断。提出的研究计划旨在通过开发新的统计理论和方法来解决这些关键挑战，包括实验设计、代理建模、模型校准、逆问题和复杂计算机模型的降维。研究方向主要集中在以下三个方面：(a)动态计算机模型的大规模反问题、功能标定和实验设计；(b)具有多变量定性反应、混合反应的计算机模型的替代模型、反问题和实验设计；以及经过审查的回复；(3)大规模多保真度计算机模型仿真，多保真度计算机模型的设计与降维。******预期的研究成果将显著推进复杂计算机模型中UQ统计方法的当前状态。新的方法将被纳入公开发布的软件中，例如R，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，包括让本科生接触昆士兰大学复杂的计算机模型，为研究生提供应用这些方法所需的高级技能，并指导博士生成为昆士兰大学统计研究的领导者