Uncertainty Quantification for Complex Computer Models

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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.