Neural Network Based Shock Detector for Numerical Solution of Conservation Laws

Dr. Yulong Xing

Abstract: In this presentation, we present a hybrid finite difference numerical method for hyperbolic conservation laws with a neural network based shock detector. One- and two-dimensional numerical examples on scalar and Euler equations are provided to demonstrate the performance of the proposed method. Comparison with the classical shock detector has also been studied, which illustrates that the neural-network based detector is able to provide a clean signal without a problem-dependent parameter. This is a joint work with Shuyi Wang, Zheng Sun, Lo-bin Chang and Dongbin Xiu (OSU).

Speaker’s Bio: Yulong Xing is an associate professor in the Department of Mathematics at Ohio State University (OSU). He received his bachelor degree from University of Science and Technology of China in 2002, and Ph.D. in Mathematics from Brown University in 2006, under the supervision of Prof. Chi-Wang Shu. Prior to joining OSU, he worked as a Postdoctoral Researcher at Courant Institute of New York University, a staff scientist at Oak Ridge National Laboratory, a joint assistant professor at University of Tennessee Knoxville, and an assistant professor at University of California-Riverside. He works in the area of numerical analysis and scientific computing, wave propagation, computational fluid dynamics.

Last Updated: September 15, 2020 - 7:46 am