Research

My research focuses on analysis and development of algorithms for high-dimensional sampling and uncertainty quantification, with applications in Bayesian inference and inverse problems. I am currently developing localization methods for sampling that utilize graphical locality to reduce computational and statistical complexity. I also work on ensemble Kalman methods for high-dimensional inference. I am broadly interested in stochastic algorithms for high-dimensional problems.

Publications

• Localized diffusion models
  Georg A. Gottwald, Shuigen Liu, Youssef Marzouk, Sebastian Reich, and Xin T. Tong, (2025). [arXiv:2505.04417]

• Stein’s method for marginals on large graphical models
  Tiangan Cui, Shuigen Liu, Xin T. Tong, (2024). [arXiv:2410.11771]

• Estimate of Koopman modes and eigenvalues with Kalman filter
  Ningxin Liu, Shuigen Liu, Xin T. Tong, and Lijian Jiang, (2024). [arXiv:2410.02815]

• Local MALA-within-Gibbs for Bayesian image deblurring with total variation prior
  Rafael Flock, Shuigen Liu, Yiqiu Dong, and Xin T. Tong, SIAM Journal on Scientific Computing, 24 (2025), pp. A2127-A2153. [arXiv]

• Dropout ensemble Kalman inversion for high dimensional inverse problems
  Shuigen Liu, Sebastian Reich and Xin T. Tong, SIAM Journal on Numerical Analysis, 63 (2025), pp. 685–715. [arXiv]