Title: Data Driven Modeling for Scientific Discovery and Digital Twins

Abstract: We present a data-driven modeling framework for scientific discovery, termed Flow Map Learning (FML). This framework enables the construction of accurate predictive models for complex systems that are not amenable to traditional modeling approaches. By leveraging measurement data and the expressiveness of deep neural networks (DNNs), FML facilitates long-term system modeling and prediction even when governing equations are unavailable. FML is particularly powerful in the context of Digital Twins, an emerging concept in digital transformation. With sufficient offline learning, FML enables the construction of simulation models for key quantities of interest (QoIs) in complex Digital Twins, even when direct mathematical modeling of the QoI is infeasible. During the online execution of a Digital Twin, the learned FML model can simulate and control the QoI without reverting to the computationally intensive Digital Twin itself. As a result, FML serves as an enabling methodology for real-time control and optimization of the physical twin, significantly enhancing the efficiency and practicality of Digital Twin applications.

Short Bio: Professor  Dongbin Xiu received his Ph.D degree from Division of Applied Mathematics of Brown University in 2004. He joined the Department of Mathematics of Purdue University in 2005. In 2013, he moved to the University of Utah as a Professor in the Department of Mathematics and Scientific Computing and Imaging (SCI) Institute. In 2016, He moved to The Ohio State University as Professor of Mathematics and Ohio Eminent Scholar. He received NSF CAREER award in 2007 and was elected to SIAM Fellow in 2023. He is the founding Associate Editor-in-Chief of the International Journal for Uncertainty Quantification (IJUQ),  founding Editor-in-Chief of Journal of Machine Learning for Modeling and Computing (JMLMC), editors-in-chief of Journal of Computational Physics. His research focuses on developing efficient numerical algorithms for uncertainty quantification and machine learning.