Shiping Zhou (周世平)

Shiping Zhou (周世平)

Michigan State University

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

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 focuses on the following areas:

  1. Nonlocal modeling and numerical methods designing
    This includes the development of nonlocal models motivated by physics, such as collision operators in palsma physics (e.g., the Fokker-Planck-Landau and Boltzmann equations), as well as nonlocal models for anomalous diffusion, fractional Laplacians, truncated fractional Laplacians, and their spatially dependent variants, as well as the design and analysis of numerical methods for these models.

  2. Shallow water moment models
    As simplified models of the Navier–Stoeks equations, these aim to capture as many physical properties as possible while keep the computational cost manageable. Examples include physical quantities such as vertical velocity, dry-wet bed dynamics, Coriolis forces, and thermal effects in fluids.

  3. Machine learning for nonlocal models
    Combining model development with numerical methods, I am interested in applying neural network techniques to learn and solve nonlocal models, including learning physical quantities (or entire models) directly from experimentally observed data.

📖 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. Nonlocal modeling of spatial fractional diffusion with truncated interaction domains and truncated kernel function singularity, S. Zhou, Y. Zhang, M. Gunzburger, submitted (2025).
  2. Moment-enhanced shallow water equations for non-slip boundary conditions, S. Zhou, J. Huang, and A. J. Christlieb, submitted (2025).
  3. Fast finite difference methods for variable-order fractional Laplacian, S. Zhou, and Y. Zhang, to be submitted (2024).
  4. 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).
  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, Comput. Phys. Commun., 318 (2026), pp. 109876.
    7. Share Link (valid till 2025-11-19)
  7. Convolutional neural network-based reduced-order modeling for parametric nonlocal PDEs, Y. Wang, S. Zhou, and Y. Zhang, Comput. Methods Appl. Mech. Eng., 444 (2025), pp. 118084.
  8. Parametric model reduction with convolutional neural networks, Y. Wang, S. Zhou, and Y. Zhang, Int. J. Numer. Anal. Mod., 21 (2024), pp. 716-738.
  9. 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.
  10. 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.

💬 Talks

  1. 2025.11, Poster: A deterministic particle method for the relativistic Landau equation, 28th International Conference on Numerical Simulation of Plasmas (ICNSP 2025), UCI, Irvine, CA.
  2. 2025.10, Invited talk: Moment-enhanced shallow water equations for non-slip boundary conditions, 2025 SIAM New York-New Jersey-Pennsylvania Section Conference, Penn State, State College, PA.
  3. 2024.12, Poster: Data-driven modeling of time-dependent nonlocal PDEs, CHaRMNET 2024 Annual Meeting, Virginia Tech, Blacksburg, VA.
  4. 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.
  5. 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.
  6. 2023.03, Poster: Numerical studies on the high-order fractional Laplacian. Pi Day Poster Session, Missouri University of Science and Technology, Rolla, MO.
  7. 2023.02, Seminar talk: Accurate and efficient spectral method for fractional wave equations. Numerical Analysis Seminar at Univrsity of Pittsburgh, Pittsburgh, PA.
  8. 2022.10, Invited talk: Accurate and efficient spectral method for fractional wave equations. The 7th Annual Meeting of SIAM Central States Section, Stillwater, OK.
  9. 2022.10, Poster: Numerical studies on the high-order fractional Laplacian. Theoretical and Applied Aspects for nonlocal Models, Workshop of BIRS, Online.
  10. 2022.04, Seminar talk: Numerical Methods for acoustic wave equations. Graduate Seminar at Missouri University of Science and Technology, Rolla, MO.
  11. 2022.03, Poster: Numerical studies on the high-order fractional Laplacian. KU Numerical Analysis Day 2022, Lawrence, KS.
  12. 2022.03, Seminar talk: Numerical studies on the high-order fractional Laplacian. Continuum Mechanics Seminar (CMS) at UNL, Online.
  13. 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.
  14. 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)