Postdoc research associate

Office: Wean Hall 7216

Department of Mathematics, Carnegie Mellon University (CMU)

Email: zecheng.zhang.math@gmail.com

- July 2022 --- Now, Postdoc Research Associate, Department of Mathematics, Carnegie Mellon University, Mentor: Prof. Hayden Schaeffer (UCLA)

- Jan 2021--- June 2022, Visiting Assistant Professor, Department of Mathematics, Purdue University, Mentor: Prof. Guang Lin.

- PhD, Mathematics, Texas A&M University, Aug 2016 --- Dec 2020.

Supervisors: Prof. Yalchin Efendiev and Prof. Eric Chung. - M.S., Mathematics, University of Alberta, Aug 2014 --- June 2016.

Thesis Directional Splitting On Grid With Local Refinement For Parabolic Problems.

Supervisors: Prof. Peter Minev and Prof. Yaushu Wong. - B.S., Applied Mathematics, Hong Kong Baptist University, Aug 2010 --- Jun 2014.

- Multiscale finite element methods
- Inverse problem
- Deep and reinforcement learning

- Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer. BelNet: Basis enhanced learning, a mesh-free neural operator.
**Preprint, 2022.**

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.
**Preprint, 2022.** - Na Ou, Zecheng Zhang, Guang Lin, A replica exchange preconditioned Crank-Nicolson Langevin
dynamic MCMC method for Bayesian inverse problems.
**Preprint, 2022.** - 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.
.**Preprint, 2022** - 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.
.**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.
.**Under revision, Journal of Scientific Computing, 2022** - 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**