Myself

Zecheng Zhang

Assistant Professor

Department of Mathematics, Florida State University (FSU)

Office: Love 311

Email: zecheng.zhang.math@gmail.com (FSU students: please contact me by my FSU email listed on the department of mathematics homepage)

News
Education and Working
I got my BSc from the Department of Mathematics at Hong Kong Baptist University. Later, I received full sponsorship to do a MSc (supervisors: Professor Yaushu Wong and Professor Peter Minev) in Mathematics at the Department of Mathematics at the University of Alberta. I then did my Ph.D. in Mathematics under the supervise of Professor Yalchin Efendiev, and Professor Eric Chung, at Texas A&M University and graduated in 2021. Following graduation, I joined the Department of Mathematics at Purdue as a visiting assistant professor under the supervise of Professor Guang Lin (Purdue). Subsequently, I moved to the Department of Mathematics at Carneigie Mellon University and did postdoc with Professor Hayden Schaeffer (UCLA). In August 2023, I joined the Department of Mathematics at Florida State University as an assistant professor.
Research Interests
Grants and Fundings
  • DOE AI For Science (DE-SC0025440), role: PI.
    • Publications And Preprints
    1. Hao Liu, Zecheng Zhang, Wenjing Liao, Hayden Schaeffer. Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study. ArXiv preprint (2024).
    2. Yuxuan Liu, Jingmin Sun, Xinjie He, Griffin Pinney, Zecheng Zhang, and Hayden Schaeffer. PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics. ArXiv preprint (2024).
    3. Derek Jollie, Jingmin Sun, Zecheng Zhang, and Hayden Schaeffer. Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model. ArXiv preprint (2024).
    4. Jingmin Sun, Zecheng Zhang, Hayden Schaeffer. LeMON: Learning to Learn Multi-Operator Networks. ArXiv preprint (2024).
    5. Jingmin Sun, Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer. Towards a Foundation Model for Partial Differential Equation: Multi-Operator Learning and Extrapolation ArXiv preprint (2024).
    6. Zecheng Zhang. MODNO: Multi Operator Learning With Distributed Neural Operators. Computer Methods in Applied Mechanics and Engineering (2024).
    7. Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu and Guang Lin. Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks. Under the first revision of Physica D: Nonlinear Phenomena (2024).
    8. Zecheng Zhang, Christian Moya, Lu Lu, Guang Lin and Hayden Schaeffer. D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators. Computer Methods in Applied Mechanics and Engineering (2024).
    9. Guang Lin, Na Ou, Zecheng Zhang, Zhidong Zhang. Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensor. Inverse Problems (2024).
    10. Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer. PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers. Neural Networks (2024).
    11. Zecheng Zhang, Christian Moya, Wing Tat Leung, Guang Lin, Hayden Schaeffer. Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE. Siam MMS (2024).
    12. Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer. A discretization-invariant extension and analysis of some deep operator networks. Journal of Computational and Applied Mathematics (2024).
    13. Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer. BelNet: Basis enhanced learning, a mesh-free neural operator. Proceedings Royal Society A: Mathematical, Physical and Engineering Sciences (2023).
      A tutorial and programming code of BelNet and operator learning is here. This BelNet tutorial is on Kaggle and we will upload a tutorial on GitHub later.
    14. Guanxun Li,Guang Lin, Zecheng Zhang, Quan Zhou. Fast Tempering for Stochastic Gradient Langevin Dynamics. ArXiv preprint (2023).
    15. Na Ou, Zecheng Zhang, Guang Lin, A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method for Bayesian inverse problems. Journal of Computational Physics (2024).
    16. Yalchin Efendiev, Wing Tat Leung, Wenyuan Li, Zecheng Zhang. Hybrid explicit-implicit learning for multiscale problems with time dependent source. Communications in Nonlinear Science and Numerical Simulation (2023).
    17. Guang Lin, Christian Moya, Zecheng Zhang. On Learning the Dynamical Response of Nonlinear Control Systems with Deep Operator Networks. Engineering Application of Artificial Intelligence (2023).
    18. Guang Lin, Zecheng Zhang, Zhidong Zhang. Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements. Inverse Problems (2022).
    19. Guang Lin, Christian Moya, Zecheng Zhang. Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs. Journal of Computational Physics (2022).
    20. Yalchin Efendiev, Wing Tat Leung, Guang Lin, Zecheng Zhang. Efficient hybrid explicit-implicit learning for multiscale problems. Journal of Computational Physics (2022).
    21. Wing Tat Leung, Guang Lin, Zecheng Zhang. NH-PINN: Neural homogenization based the physics-informed neural network for the multiscale problems. Journal of Computational Physics (2022).
    22. Guang Lin, Yating Wang, Zecheng Zhang. Multi-variance replica exchange stochastic gradient MCMC for inverse and forward Bayesian physics-informed neural network. Journal of Computational Physics (2022).
    23. Liu Liu, Tieyong Zeng, Zecheng Zhang. A deep neural network approach on solving the linear transport model under diffusive scaling. ArXiv preprint (2021).
    24. Eric Chung, Yalchin Efendiev, Sai-Mang Pun, Zecheng Zhang. Computational multiscale methods for parabolic wave approximations in heterogeneous media. Applied Mathematics and Computation (2022).
    25. Eric Chung, Yalchin Efendiev, Wing Tat Leung, Sai-Mang Pun and Zecheng Zhang. Multi-agent reinforcement learning aided sampling algorithms for a class of multiscale inverse problems. Journal of Scientific Computing (2023).
    26. Boris Chetverushkin, Eric Chung, Yalchin Efendiev, Sai-Mang Pun and Zecheng Zhang. Computational multiscale methods for quasi-gas dynamic equations. Journal of Computational Physics (2020).
    27. Eric Chung, Wing Tat Leung, Sai-Mang Pun and Zecheng Zhang. A multi-stage deep learning based algorithm for multiscale model reduction. Journal of Computational and Applied Mathematics (2020).
    28. Eric Chung, Yalchin Efendiev, Wing Tat Leung, Zecheng Zhang. Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations. Mathematics (2020).
    Seminars and Workshops
    Fall 2024 ACM seminar, Time: 3:05 pm to 4:05 pm (easten time). Location: zoom or Love 0231. Please contact me if you are interested in giving a talk.
    Teaching
  • Spring 2024, Calculus II.
  • Fall 2023, Multivariate calculus.
  • Spring 2023, 21-344 Numerical Linear Algebra.
  • Fall 2022, 21-670 Linear Algebra for Data Science.
  • Spring 2022, Linear Algebra at Purdue university.
  • Fall 2021, ODE.

    Useful Links (construction in progress)