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)

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

- Guest Editor of the MDPI Mathematics Special Issue “Trends and Prospects in Mathematical and Scientific Machine Learning”.

- Jingmin Sun, Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer. Towards a Foundation Model for Partial Differential Equation: Multi-Operator Learning and Extrapolation ArXiv preprint (2024).
- Zecheng Zhang. MODNO: Multi Operator Learning With Distributed Neural Operators. ArXiv preprint (2024).
- Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu and Guang Lin. Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks. ArXiv preprint (2024).
- 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).
- Guang Lin, Na Ou, Zecheng Zhang, Zhidong Zhang. Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensor. Inverse Problems (2024).
- Yuxuan Liu, Zecheng Zhang, Hayden Schaeffer. PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers. ArXiv preprint (2023).
- 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).
- Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer. A discretization-invariant extension and analysis of some deep operator networks. ArXiv preprint (2023).
- 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. - Guanxun Li, Guang Lin, Zecheng Zhang, Quan Zhou. Fast Tempering for Stochastic Gradient Langevin Dynamics. ArXiv preprint (2023).
- Na Ou, Zecheng Zhang, Guang Lin, A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method for Bayesian inverse problems. Under the first round review of Journal of Computational Physic.
- 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).
- 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).
- 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).
- 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).
- Yalchin Efendiev, Wing Tat Leung, Guang Lin, Zecheng Zhang. Efficient hybrid explicit-implicit learning for multiscale problems. Journal of Computational Physics (2022).
- 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).
- 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).
- Liu Liu, Tieyong Zeng, Zecheng Zhang. A deep neural network approach on solving the linear transport model under diffusive scaling. ArXiv preprint (2021).
- Eric Chung, Yalchin Efendiev, Sai-Mang Pun, Zecheng Zhang. Computational multiscale methods for parabolic wave approximations in heterogeneous media. Applied Mathematics and Computation (2022).
- 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).
- 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).
- 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).
- Eric Chung, Yalchin Efendiev, Wing Tat Leung, Zecheng Zhang. Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations. Mathematics (2020).