Juncai He

About

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.

 

Research Interest

  • Deep Learning, Stochastic Optimization.

  • Numerical Analysis, Finite Element Methods, Multigrid Methods.

My research focuses on mathematical analysis, algorithm development, and their applications in machine learning and scientific computing, spanning both data and physical sciences. My Ph.D. training was grounded in classical numerical methods for partial differential equations (PDEs), with a particular emphasis on finite element methods (FEM) and multigrid methods. Armed with this solid foundation in numerical PDEs and scientific computing, my primary research objective is to explore deep learning models and algorithms through the lens of numerical PDEs and geometry. This approach aims to foster a comprehensive understanding and innovative advancement of these models, covering theoretical foundations, algorithmic strategies, and practical applications. From my Ph.D. program to the present, and continuing into the foreseeable future, my research efforts and aspirations are principally centered on three interrelated themes:

  1. Mathematical analysis of deep neural networks (DNNs) from a finite element perspective;
  2. Development of theories, algorithms, and applications for convolutional neural networks (CNNs) and Transformers, drawing inspiration from multigrid structures;
  3. Investigation into the learning of data with low-dimensional structures.

 

Education Profile

 

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