DDPS | Data-driven modeling of unknowns systems with deep neural networks by Dongbin Xiu

We present a framework of predictive modeling of unknown system from measurement data. The method is designed to discover/approximate the unknown evolution operator, i.e., flow map, behind the data. Deep neural network (DNN) is employed to construct such an approximation. Once an accurate DNN model for the evolution operator is constructed, it serves as a predictive model for the unknown system and enables us to conduct system analysis. We demonstrate that flow map learning (FML) approach is applicable for modeling a wide class of problems, including dynamical systems, systems with missing variables and hidden parameters, as well as partial differential equations (PDEs).

Bio: Dongbin Xiu received his Ph.D degree from Division of Applied Mathematics of Brown University in 2004. He conducted postdoctoral studies in Los Alamos National Laboratory, Princeton University, and Brown University, before joining 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 (SCI) Institute. In 2016, He moved to The Ohio State University as Professor of Mathematics and Ohio Eminent Scholar. He has received NSF CAREER award in 2007, as well as a number of teaching awards at Purdue. He has served on the editorial board of several journals, including SIAM Journal on Scientific Computing and Journal of Computational Physics. He is the founding Associate Editor-in-Chief of the International Journal for Uncertainty Quantification (IJUQ), and the founding Editor-in-Chief of Journal of Machine Learning for Modeling and Computing (JMLMC). His research focuses on developing efficient numerical algorithms for uncertainty quantification, stochastic computing, and machine learning.

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