Ph.D., Computational Mathematics, Peking University, 2014-2019
Advisors: Prof. Jinchao Xu and Prof. Jun Hu
Thesis: Finite Element Methods and Deep Neural Networks
Visiting Ph.D. Research Scholar, Center for Computational Mathematics and Application (CCMA), Department of Mathematics, The Pennsylvania State University, Feb. 2016 - Jul. 2016, Oct. 2017 - Mar. 2018, and Mar. 2019 - May 2019.
B.S., Mathematics and Applied Mathematics, Sichuan University, 2010-2014.
I am currently a research scientist in Computer, Electrical and Mathematical Science and Engineering Division (CEMSE) at King Abdullah University of Science and Technology (KAUST).
I received a B.S. degree in Mathematics and Applied Mathematics from Sichuan University in 2014. In the Summer of 2019, I received my Ph.D. degree in Computational Mathematics under the supervision of Prof. Jinchao Xu and Prof. Jun Hu at Peking University in Beijing, China. From 2019 to 2020, I worked as a Postdoctoral Scholar supervised by Prof. Jinchao Xu in The Center for Computational Mathematics and Application (CCMA) in the Department of Mathematics at The Pennsylvania State University, University Park. From 2020 to 2022, I was an R.H. Bing postdoctoral fellow working with Prof. Richard Tsai and Prof. Rachel Ward in the Department of Mathematics at UT Austin, Austin.
Deep Learning, Stochastic Optimization.
Numerical Analysis, Finite Element Methods, Multigrid Methods.
My research interests are in algorithm development and theoretical analysis for machine learning and numerical methods for partial differential equations (PDEs). I have received broad and in-depth training in finite elements, multigrid (MG) methods, and machine learning. I have studied the finite element exterior calculus (FEEC) method both for its theoretical analysis and also application in structure-preserving discretization for multi-physical systems. I have also applied techniques from numerical PDEs for understanding and improving deep learning models and algorithms in data science. In particular, I have worked on three different but related topics:
finite element methods and deep neural networks (DNNs);
multigrid methods and architecture of convolutional neural networks;
stochastic optimization methods.