Optimal Low-rank Approximations of Bayesian Linear Inverse Problems. - Alessio Spantini; Antti Solonen; Tiangang Cui; James Martin; Luis Tenorio; Youssef M. Marzouk (SIAM J. Sci. Comput., 2015)

Dimension-independent likelihood-informed MCMC. - Tiangang Cui; Kody J. H. Law; Youssef M. Marzouk (J. Comput. Phys., 2016)

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction. - Tiangang Cui; Youssef M. Marzouk; Karen Willcox (J. Comput. Phys., 2016)

Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems. - Alessio Spantini; Tiangang Cui; Karen Willcox; Luis Tenorio; Youssef M. Marzouk (SIAM J. Sci. Comput., 2017)

Bayesian Inverse Problems with l1 Priors: A Randomize-Then-Optimize Approach. - Zheng Wang; Johnathan M. Bardsley; Antti Solonen; Tiangang Cui; Youssef M. Marzouk (SIAM J. Sci. Comput., 2017)

Mathematical Modelling of Genetic Network for Regulating the Fate Determination of Hematopoietic Stem Cells. - Siyuan Wu; Tiangang Cui; Tianhai Tian (BIBM, 2018)

A Stein variational Newton method. - Gianluca Detommaso; Tiangang Cui; Youssef M. Marzouk; Alessio Spantini; Robert Scheichl (NeurIPS, 2018)

Stein Variational Online Changepoint Detection with Applications to Hawkes Processes and Neural Networks. - Gianluca Detommaso; Hanne Hoitzing; Tiangang Cui; Ardavan Alamir (CoRR, 2019)

Multilevel Dimension-Independent Likelihood-Informed MCMC for Large-Scale Inverse Problems. - Tiangang Cui; Gianluca Detommaso; Robert Scheichl (CoRR, 2019)

Optimization-Based MCMC Methods for Nonlinear Hierarchical Statistical Inverse Problems. - Johnathan M. Bardsley; Tiangang Cui (CoRR, 2020)

Scalable Optimization-Based Sampling on Function Space. - Johnathan M. Bardsley; Tiangang Cui; Youssef M. Marzouk; Zheng Wang (SIAM J. Sci. Comput., 2020)

Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems. - Tiangang Cui; Olivier Zahm (CoRR, 2021)

Conditional Deep Inverse Rosenblatt Transports. - Tiangang Cui; Sergey Dolgov; Olivier Zahm (CoRR, 2021)

Optimization-Based Markov Chain Monte Carlo Methods for Nonlinear Hierarchical Statistical Inverse Problems. - Johnathan M. Bardsley; Tiangang Cui (SIAM/ASA J. Uncertain. Quantification, 2021)

Identification of community structure-based brain states and transitions using functional MRI. - Lingbin Bian; Tiangang Cui; B. T. Thomas Yeo; Alex Fornito; Adeel Razi; Jonathan Keith (NeuroImage, 2021)

Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems. - Tiangang Cui; Xin Tong; Olivier Zahm (CoRR, 2022)

Deep importance sampling using tensor-trains with application to a priori and a posteriori rare event estimation. - Tiangang Cui; Sergey Dolgov; Robert Scheichl (CoRR, 2022)

A variational neural network approach for glacier modelling with nonlinear rheology. - Tiangang Cui; Zhongjian Wang; Zhiwen Zhang 001 (CoRR, 2022)

Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports. - Tiangang Cui; Sergey Dolgov (Found. Comput. Math., 2022)

Certified dimension reduction in nonlinear Bayesian inverse problems. - Olivier Zahm; Tiangang Cui; Kody J. H. Law; Alessio Spantini; Youssef M. Marzouk (Math. Comput., 2022)

Tensor-based Methods for Sequential State and Parameter Estimation in State Space Models. - Yiran Zhao 005; Tiangang Cui (CoRR, 2023)

Self-reinforced polynomial approximation methods for concentrated probability densities. - Tiangang Cui; Sergey Dolgov; Olivier Zahm (CoRR, 2023)

Bernstein approximation and beyond: proofs by means of elementary probability theory. - Tiangang Cui; Friedrich Pillichshammer (CoRR, 2023)

Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction. - Tiangang Cui; Sergey Dolgov; Olivier Zahm (J. Comput. Phys., 2023)

Sequential transport maps using SoS density estimation and α-divergences. - Benjamin Zanger; Tiangang Cui; Martin Schreiber 001; Olivier Zahm (CoRR, 2024)

Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities. - Matthew T. C. Li; Tiangang Cui; Fengyi Li; Youssef M. Marzouk; Olivier Zahm (CoRR, 2024)

ell infty-approximation of localized distributions. - Tiangang Cui; Shuigen Liu; Xin Tong (CoRR, 2024)

Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds. - Tiangang Cui; Alex Gorodetsky (CoRR, 2024)

A tensor-train reduced basis solver for parameterized partial differential equations. - Nicholas Mueller; Yiran Zhao; Santiago Badia; Tiangang Cui (CoRR, 2024)

Tensor-train methods for sequential state and parameter learning in state-space models. - Yiran Zhao 005; Tiangang Cui (J. Mach. Learn. Res., 2024)

Deep Importance Sampling Using Tensor Trains with Application to a Priori and a Posteriori Rare Events. - Tiangang Cui; Sergey Dolgov; Robert Scheichl (SIAM J. Sci. Comput., 2024)

Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems. - Tiangang Cui; Hans De Sterck; Alexander D. Gilbert; Stanislav Polishchuk; Robert Scheichl (J. Sci. Comput., 2024)

Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation. - Tiangang Cui; Josef Dick; Friedrich Pillichshammer (Adv. Comput. Math., 2025)

Subspace accelerated measure transport methods for fast and scalable sequential experimental design, with application to photoacoustic imaging. - Tiangang Cui; Karina Koval; Roland Herzog; Robert Scheichl (CoRR, 2025)

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids. - Nicholas Mueller; Yiran Zhao; Santiago Badia; Tiangang Cui (J. Comput. Appl. Math., 2026)