Shiping Zhou (周世平)

Shiping Zhou (周世平)

Michigan State University

Welcome! I am Shiping Zhou. Starting from August 2024, I will be a postdoctoral research associate in the Department of Computational Mathematics, Science and Engineering (CMSE), under the supervision of Dr. Andrew Christlieb, at Michigan State University (MSU).

Before joining MSU, I received my Ph.D. in the Department of Mathematics and Statistics at Missouri University of Science and Technology in May 2024, under the guidance of Dr. Yanzhi Zhang.

My research primarily centers on two main areas:

  1. Nonlocal problems: This encompasses the development of accurate and efficient numerical schemes for solving nonlocal problems. Applications of these models including various fields such as wave propagation in heterogeneous media in geophysics, anomalous diffusion in biology, and dark matter in cosmology.
  2. Data-driven modeling: In this area, I utilize neural network techniques to solve time-dependent classical and nonlocal PDEs. I explore using machine learning to learn the nonlocal kernels and their applications in material science.

📖 Educations

  • 2019.08 - 2024.05, Ph.D. in Mathematics (Computational and Applied Emphasis), Missouri University of Science and Technology, Rolla, MO

    Advisor: Prof. Yanzhi Zhang

  • 2016.09 - 2019.06, M.S. in Computational Mathematics, Shandong University, China

    Advisor: Prof. Fuzheng Gao

  • 2012.09 - 2016.07, B.S. in Mathematics and Applied Mathematics, Anhui University of Technology, China

🎖 Awards

  • 2024 Gaoxiong Gan Scholarship Fund, Missouri University of Science and Technology
  • 2023 8th Annual Meeting of SIAM Central State Section Travel Award
  • 2023 Paul W. Eloe Graduate Research Award, Missouri University of Science and Technology
  • 2023 Gaoxiong Gan Scholarship Fund, Missouri University of Science and Technology
  • 2023 First place at the Pi Day Celebration Poster Session, Missouri University of Science and Technology
  • 2023 Graduate Education Travel Fund, Missouri University of Science and Technology
  • 2022 Paul W. Eloe Graduate Research Award, Missouri University of Science and Technology
  • 2022 Nonlocal School of Fractional Equations NSFE Travel Award
  • 2022 Mathematics and Statistics Alumni Endowed Scholarship, Missouri University of Science and Technology
  • 2022 Gaoxiong Gan Scholarship Fund, Missouri University of Science and Technology
  • 2022 7th Annual Meeting of SIAM Central State Section Travel Award

📝 Publications

  1. Fast finite difference methods for variable-order fractional Laplacian, S. Zhou, and Y. Zhang, to be submitted (2024).

  2. Data-driven approach for the solutions of time-dependent PDEs using convolutional neural network, S. Zhou, Y. Li, and Y. Zhang, to be submitted (2024).

  3. Convolutional neural network-based reduced order modeling for parametric nonlocal PDEs, Y. Wang, S. Zhou, and Y. Zhang, submitted (2024).

  4. Parametric model reduction with convolutional neural networks, Y. Wang, S. Zhou, and Y. Zhang, submitted (2024).

  5. Analytical and computational aspects of the high-order fractional Laplacian, J.P. Borthagaray, Y. Wu, S. Zhou, and Y. Zhang, preprint (2023).

  6. Fourier pseudospectral methods for the spatial variable-order fractional wave equations, Y. Zhang, X. Zhao, S. Zhou, (2023), submitted. arXiv

  7. A novel spectral method for space-fractional PDEs with the fractional Laplacians, S. Zhou and Y. Zhang, Comput. Math. Appl., 168 (2024), pp.133–147. doi:10.1016/j.camwa.2024.06.001

  8. Weak Galerkin Finite Element Method with Second-order accuracy in time for parabolic problems, S. Zhou, F. Gao, B. Li, and Z. Sun, Appl. Math. Lett., 90(2019), pp.118-123. doi:10.1016/j.aml.2018.10.023

💬 Talks

  1. 2023.10, Invited talk: A novel and simple spectral method for nonlocal PDEs with fractional Laplacian. The 8th Annual Meeting of SIAM Central States Sections, Lincoln, NE.
  2. 2023.04, Seminar talk: A novel and simple spectral method for nonlocal PDEs with fractional Lpalcian. Graduate Seminar at Missouri University of Science and Technology, Rolla, MO.
  3. 2023.03, Poster: Numerical studies on the high-order fractional Laplacian. Pi Day Poster Session, Missouri University of Science and Technology, Rolla, MO.
  4. 2023.02, Seminar talk: Accurate and efficient spectral method for fractional wave equations. Numerical Analysis Seminar at Univrsity of Pittsburgh, Pittsburgh, PA.
  5. 2022.10, Invited talk: Accurate and efficient spectral method for fractional wave equations. The 7th Annual Meeting of SIAM Central States Section, Stillwater, OK.
  6. 2022.10, Poster: Numerical studies on the high-order fractional Laplacian. Theoretical and Applied Aspects for nonlocal Models, Workshop of BIRS, Online.
  7. 2022.04, Seminar talk: Numerical Methods for acoustic wave equations. Graduate Seminar at Missouri University of Science and Technology, Rolla, MO.
  8. 2022.03, Poster: Numerical studies on the high-order fractional Laplacian. KU Numerical Analysis Day 2022, Lawrence, KS.
  9. 2022.03, Seminar talk: Numerical studies on the high-order fractional Laplacian. Continuum Mechanics Seminar (CMS) at UNL, Online.
  10. 2021.11, Invited talk: Numerical studies on the high-order fractional Laplacian. 4th Annual Meeting of the SIAM Texas-Louisiana Section, South Padre Island, TX.
  11. 2021.10, Contributed talk: Numerical studies on the high-order fractional Laplacian. Midwest Numerical Analysis Day 2021, Rolla, MO.

👨🏻‍🏫 Teaching

Missouri University of Science and Technology

  • Instructor (Spring 2023)

    Elementary Differential Equations (MATH 3304) (98 students in total)

  • Co-Instructor (Fall 2020)

    Mathematics Calculus for Engineers I (MATH 1214)

  • Grader (Spring 2020)

    Mathematics Calculus for Engineers I (MATH 1214)

  • Grader (Fall 2019)

    Mathematics Calculus for Engineers I (MATH 1214)