Chenguang Duan

I recently obtained my Ph.D. from the School of Mathematics and Statistics, Wuhan University, where I was very fortunate to be advised by Prof. Jerry Zhijian Yang. Throughout my research, I was also fortunate to work closely with Prof. Yuling Jiao. I earned my Bachelor’s degree in Mathematics from Wuhan University as well. In the near future, I will be joining RWTH Aachen University as a postdoctoral researcher at Institute of Geometry and Practical Mathematics, working with Prof. Markus Bachmayr and Prof. Wolfgang Dahmen.

My research interests lie at the intersection of computational mathematics, statistics, and machine learning, with a particular emphasis on learning theory, generative models, and scientific machine learning.

Here is my Google Scholar page.

Email: cgduan.math@gmail.com (Preferred), cgduan.math@whu.edu.cn

Research interests

Statistical learning and deep learning theory
Generative models and sampling
Machine learning for scientific computing
Inverse problems and uncertainty quantification

Research

Google Scholar (All of my publications have authors listed in alphabetical order)

Ongoing Work

Nonlinear Assimilation via Score-based Sequential Langevin Sampling

Zhao Ding, Chenguang Duan, Yuling Jiao, Jerry Zhijian Yang, Cheng Yuan, and Pingwen Zhang

[arXiv] [PDF] [code] [slides]

Abstract

This paper presents score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating prediction and update steps, leveraging dynamic models for state prediction while incorporating observational data through score-based Langevin Monte Carlo during updates. To address challenges in posterior sampling, we introduce an annealing strategy within the update mechanism. We provide theoretical guarantees for SSLS convergence in total variation (TV) distance under certain conditions, providing insights into error behavior with respect to key hyper-parameters. Our numerical experiments across challenging scenarios -- including high-dimensional systems, strong nonlinearity, and sparse observations -- demonstrate the robust performance of the proposed method. Furthermore, SSLS effectively quantifies the uncertainty associated with the estimated states, making it particularly valuable for the error calibration.

Bibtex


@misc{ding2025nonlinear,
      title={Nonlinear Assimilation via Score-based Sequential {S}angevin Sampling}, 
      author={Zhao Ding and Chenguang Duan and Yuling Jiao and Jerry Zhijian Yang and Cheng Yuan and Pingwen Zhang},
      year={2025},
      note={arXiv:2411.13443},
}

Characteristic Learning for Provable One Step Generation

Zhao Ding, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, and Pingwen Zhang

[arXiv] [PDF] [code]

Selected Publications

Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network

Zhao Ding, Chenguang Duan, Yuling Jiao, and Jerry Zhijian Yang

IEEE Transactions on Information Theory (2025)

* Awarded the 18th East Asia Section of SIAM (EASIAM) Student Paper Prize, Second Prize

[Journal] [arXiv] [PDF] [slides]

Recovering the Source Term in Elliptic Equation via Deep Learning: Method and Convergence Analysis

Chenguang Duan, Yuling Jiao, Jerry Zhijian Yang, and Pingwen Zhang

East Asian Journal on Applied Mathematics (2024)