Juncai He

何俊材
Juncai He 

Juncai He


R.H. Bing Postdoctoral Fellow
Department of Mathematics
The University of Texas at Austin
2515 Speedway, PMA
Austin, TX 78712

Phone: +1 616-227-5319
Email: jhe@utexas.edu

About me

I am currently a R.H. Bing postoctoral fellow in the Department of Mathematics at UT Austin.

I received the B.S. degree in Mathematics and Applied Mathematics from Sichuan University in 2014. In 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 at Beijing, China. From 2019 to 2020, I worked as a Postdoctoral Scholar suprevised 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.

Research

  • 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 element, multigrid (MG) methods and machine learning. I have studied the finite element exterior calculus (FEEC) method both for its theoretical analysis and also the 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:

  1. finite element methods and deep neural networks (DNNs);

  2. multigrid methods and architectures of convolutional neural networks;

  3. stochastic optimization methods.

Publications

Education

Teaching

Instructor at UT Austin for:

Teaching assistant at Penn State and Peking University for:

  • An Introduction to Deep Learning, Penn State Education Abroad Summer Course, Jul. 6-27, 2019

  • An Introduction for Applied Mathematics, Peking University, Feb. 2017 - Jun. 2017

  • Advanced Linear Algebra I, Peking University, Sept. 2016 - Jan. 2017

  • Calculus, Peking University, Sept. 2015 - Jan. 2016

The Workshops/ Minisymposium Organized

Presentations