Speaker: Di Qi, Purdue University
Title: Reduced-Order Moment Closure Models for Uncertainty Quantification and Data Assimilation
Abstract: We present a new strategy for the statistical forecasts of multiscale nonlinear systems involving non-Gaussian probability distributions. The capability of using reduced-order models to capture key statistical features is investigated. A closed stochastic-statistical modeling framework is proposed using a high-order statistical closure enabling accurate prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. A new efficient ensemble forecast algorithm is developed dealing with the nonlinear multiscale coupling mechanism as a characteristic feature in high-dimensional turbulent systems. To address challenges associated with closely coupled spatio-temporal scales in turbulent states and expensive large ensemble simulation for high-dimensional complex systems, we introduce efficient computational strategies using the random batch method. Effective nonlinear ensemble filters are developed based on the nonlinear coupling structures of the explicit stochastic and statistical equations, which satisfy an infinite-dimensional Kalman-Bucy filter with conditional Gaussian dynamics. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the new reduced-order model in various dynamical regimes of the flow field with distinct statistical structures.
Bio: Di Qi is currently an Assistant Professor at the Department of Mathematics, Purdue University. He is interested in the general area of applied and computational mathematics, where mathematical tools and numerical methods are developed to address problems in science and engineering. His current research topics mainly focus on numerical methods for PDEs, stochastic and statistical analysis, and uncertainty quantification. I'm working on model reduction strategies, statistical control methods, statistical stability analysis, turbulent diffusion, and data assimilation for complex turbulent dynamical systems, including their applications in fluid dynamics, atmosphere-ocean science, and plasma physics. For more details, see his research projects and publication list.
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