Menu
Home
CV
Useful links
2020 ML Workshop
Math497 Summer 2020
Multigrid.org
Jemdoc

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 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.

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 architecture of convolutional neural networks;

  3. stochastic optimization methods.

Publications

  • J. He, L. Li, J. Xu. Approximation Properties of Deep ReLU CNNs. ArXiv: 2109.00190, 2021.

  • Q. Chen, W. Hao, J. He. A Weight Initialization Based on the Linear Product Structure for Neural Networks. ArXiv: 2109.00125, 2021.

  • J. He, L. Li, J. Xu. ReLU Deep Neural Networks from the Hierarchical Basis Perspective. ArXiv: 2105.04156, 2021.

  • Q. Chen, W. Hao, J. He. Power Series Expansion Neural Network. ArXiv: 2102.13221, 2021.

  • J. He, X. Jia, J. Xu, L. Zhang and L. Zhao. Make ell_1 Regularization Effective in Training Sparse CNN. Computational Optimization and Applications. 2020. https:doi.org10.1007s10589-020-00202-1 ArXiv: 1807.04222v4.

  • J. He, L. Li, J. Xu, and C. Zheng. ReLU Deep Neural Networks and linear Finite Elements. Journal of Computational Mathematics. 38(3): 502-527, 2020. doi:10.4208/jcm.1810-m2018-0096.

  • J. He, K. Hu, J. Xu. Generalized Gaffney Inequality and Discrete Compactness for Discrete Differential Forms. Numerische Mathematik. 2019. https:doi.org10.1007s00211-019-01076-0.

  • J. He and J. Xu. MgNet: A Unified Framework of Multigrid and Convolutional Neural Network. Science China Mathematics. 62(7): 1331–1354, 2019. https:doi.org10.1007s11425-019-9547-2.

  • J. He, Y. Chen, L. Zhang and J. Xu. Constrained Linear Data-feature Mapping in Image Classification. ArXiv: 1911.10428, 2019.

Education

Teaching

Instructor at UT Austin for:

Teaching assistant at Penn State and Peking University for:

  • MATH 497: Deep Learning Algorithms and Analysis , Penn State University, Jul. 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