Data-Driven Modeling of Unknown Systems with Deep Neural Networks

Abstract: We present a framework of predictive modeling of unknown systems from measurement data.  The method is designed to discover/approximate the unknown evolution operator behind the data.  Deep neural network (DNN) is employed to construct such an approximation.  Once an accurate DNN model for evolution operator is constructed, it serves as a predictive model for the unknown system and enables us to conduct system analysis.  We demonstrate that residual network is particularly suitable for modeling autonomous dynamical systems.  Extensions to other types of systems will be discussed, including non-autonomous systems, systems with uncertain parameters, and more importantly, systems with missing variables, as well as partial differential equations.

Speaker’s Bio: Dongbin Xiu received his Ph.D. degree from the Division of Applied Mathematics of Brown University in 2004, and joined the Department of Mathematics of Purdue University as an Assistant Professor in the fall of 2005.  He was promoted to the rank of Associate Professor in 2009 and to Full Professor in 2012.  In 2013, he moved to the University of Utah as a Professor in the Department of Mathematics and Scientific Computing and Imaging  Institute.  In 2016, He moved to Ohio State University as a Professor of Mathematics and Ohio Eminent Scholar.  His research focuses on developing efficient numerical algorithms for uncertainty quantification, stochastic computing, and machine learning.  He received the National Science Foundation CAREER award in 2007 and was selected as a Society of Industrial and Applied Mathematics Fellow in 2023.