Dongbig Xiu, PhD | The Ohio State University
TITLE:Data Driven Governing Equations Recovery with Deep Neural Networks
We present effective numerical algorithms for recovering unknown governing differential equations from measurement data. Upon recasting the problem into a function approximation problem, we discuss several important aspects for accurate recovery/approximation. Most notably, we discuss the importance of using a large number of short bursts of trajectory data, rather than using data from a single long trajectory. We also present several recovery strategies using deep neural networks (DNNs), especially those based on reside network (ResNet). We then present an extensive set of numerical examples of both linear and nonlinear systems to demonstrate the properties and effectiveness of our equation recovery algorithms.
Dongbin Xiu received his Ph.D degree from the Division of Applied Mathematics of Brown University in 2004. He conducted post doctoral 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 is 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. His research focuses on developing efficient numerical algorithms for uncertainty quantification, stochastic computing, and machine learning.