Presentation: Prof. Dr. Pengfei Wei

Bayesian numerics for uncertainty quantification, August 1, 3:00 pm, room 116

Uncertainty quantification (UQ) is the process of quantitative modeling and estimation of uncertainties presented in mathematical modeling, simulations, and measurements of the real world, and has witnessed increasing importance in many fields, such as engineering structures, which rely on numerical simulations for reliable decision-making and design. Addressing alternative challenging numerical problems, such as uncertainty propagation, Bayesian model updating, sensitivity analysis, and uncertainty-based design optimization, with high efficiency and accuracy guarantee, has long been recognized as the core of UQ. In this lecture, I would to introduce some of our developments for addressing the above numerical tasks with a state-of-the-art numerical analysis methodology framework called Bayesian numerics, which is an extension of Bayesian machine learning. This lecture consists of three main parts. First, a conceptual introduction to UQ for engineering structures, including the sources, categorization, and modeling of uncertainties, as well as different numerical computation problems involved in UQ. Second, a brief introduction to our developments of addressing alternative numerical tasks in UQ, including integration, optimization, failure probability estimation, probabilistic analysis of PDEs, and sensitive indices estimation. Third, of special concern, the concept of Collaborative and Adaptive Bayesian Optimization (CABO) is presented as a general method for efficiently addressing the nested numerical problems involved in UQ, and of special concern is the propagation of the probability boxes for modeling hybrid uncertainties consisting of both aleatory and epistemic elements. By performing active learning in the augmented space and Bayesian inference in the marginal subspaces, it is shown that CABO can solve alternative types of nested problems with high efficiency and global convergence.



Pengfei Wei
School of Power and Energy, Northwestern Polytechnical University, Xi’an, PR China



Pengfei Wei is an associate professor of the School of Power and Energy, at Northwestern Polytechnical University of China. Dr. Wei’s research is mainly on uncertainty quantification for engineering structures, and as the first/corresponding author, he has published more than 40 journal papers in this area. He is the Editorial board member of several international journals including Reliability Engineering and System Safety, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A Civil Engineering, and Part B Mechanical Engineering. He is a fellow of the Alexander von Humboldt Foundation.


Additional information

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