Research

My reseach focuses:

  • Multiscale modeling and simulation
  • Mathematics of machine learning
  • Scientific machine learning

Active grants:

  • DOE AI For Science (DE-SC0025440)

Publications and preprints.

  1. Zecheng Zhang, Liu Hao, Wenjing Liao, Guang Lin. Coefficient-to-Basis Network: A Fine-Tunable Operator Learning Framework for Inverse Problems with Adaptive Discretizations and Theoretical Guarantees. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (2025).
  2. Zecheng Zhang, Christian Moya, Lu Lu, Guang Lin and Hayden Schaeffer. DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuning. ArXiv preprint (2024).
  3. Hao Liu, Zecheng Zhang, Wenjing Liao, Hayden Schaeffer. Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study. ArXiv preprint (2024).
  4. 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. Neurips 2024 Workshop Foundation Models for Science.
  5. 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).
  6. Jingmin Sun, Zecheng Zhang, Hayden Schaeffer. LeMON: Learning to Learn Multi-Operator Networks. ArXiv preprint (2024).
  7. Jingmin Sun, Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer. Towards a Foundation Model for Partial Differential Equation: Multi-Operator Learning and Extrapolation. Physics Review E (2024).
  8. Zecheng Zhang. MODNO: Multi Operator Learning With Distributed Neural Operators. Computer Methods in Applied Mechanics and Engineering (2024).
  9. Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu and Guang Lin. Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks. Physica D: Nonlinear Phenomena (2025).
  10. 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).
  11. Guang Lin, Na Ou, Zecheng Zhang, Zhidong Zhang. Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensor. Inverse Problems (2024).
  12. Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer. PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers. Neural Networks (2024).
  13. 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).
  14. 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).
  15. 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.
  16. Guanxun Li,Guang Lin, Zecheng Zhang, Quan Zhou. Fast Tempering for Stochastic Gradient Langevin Dynamics. ArXiv preprint (2023).
  17. 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).
  18. 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).
  19. 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).
  20. 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).
  21. 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).
  22. Yalchin Efendiev, Wing Tat Leung, Guang Lin, Zecheng Zhang. Efficient hybrid explicit-implicit learning for multiscale problems. Journal of Computational Physics (2022).
  23. 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).
  24. 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).
  25. Liu Liu, Tieyong Zeng, Zecheng Zhang. A deep neural network approach on solving the linear transport model under diffusive scaling. ArXiv preprint (2021).
  26. Eric Chung, Yalchin Efendiev, Sai-Mang Pun, Zecheng Zhang. Computational multiscale methods for parabolic wave approximations in heterogeneous media. Applied Mathematics and Computation (2022).
  27. 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).
  28. 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).
  29. 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).
  30. Eric Chung, Yalchin Efendiev, Wing Tat Leung, Zecheng Zhang. Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations. Mathematics (2020).