Applied Math Colloquium with Prof Dongbin Xiu, Ohio State University

Speaker: Prof Dongbin Xiu,Ohio State University

Title: Observable Dynamics: Delay Closure and Flow Map Learning 

Abstract: We present a mathematical and numerical framework for modeling the dynamics of observables in complex systems. We establish that, for a broad class of systems, the evolution of a given observable can be represented by a finite history of its past values, leading to closed delay equations with minimal memory without explicit access to the underlying state variables. This result provides a mathematical foundation for incorporating temporal history dependence into data-driven numerical methods, particularly the Flow Map Learning (FML) algorithm. Numerical examples demonstrate the efficacy of FML for efficient long-time prediction of observable dynamics. 

Bio: Dongbin Xiu received his Ph.D. in Applied Mathematics from Brown University in 2004. He joined the Department of Mathematics at Purdue University in 2005 and moved to the University of Utah in 2013. In 2016, he joined The Ohio State University as a Professor of Mathematics and an Ohio Eminent Scholar. 
Dr. Xiu received the NSF CAREER Award in 2007 and was elected a SIAM Fellow in 2023. He has served on editorial boards of many journals and is currently the Editor-in-Chief of the Journal of Computational Physics. Additionally, he is the founding Associate Editor-in-Chief of the International Journal for Uncertainty Quantification (IJUQ) and the founding Editor-in-Chief of the Journal of Machine Learning for Modeling and Computing (JMLMC). 
His current research focuses on developing efficient numerical methods for data-driven modeling, scientific machine learning, Digital Twins, and uncertainty quantification. 

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