publications

2025

1. AAP

   Convergence Speed and Approximation Accuracy of Numerical MCMC

   Cui, Tiangang, Dong, Jing, Jasra, Ajay, and Tong, Xin T

   Advances in Applied Probability , in press, 2025 arXiv
2. ACM

   Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation

   Cui, Tiangang, Dick, Josef, and Pillichshammer, Friedrich

   Advances in Computational Mathematics, accepted, 2025 arXiv
3. Bernstein approximation and beyond: proofs by means of elementary probability theory

   Cui, Tiangang, and Pillichshammer, Friedrich

   Elemente der Mathematik, in press, 2025 arXiv

2024

1. SISC

   Deep importance sampling using tensor-trains with application to a priori and a posteriori rare event estimation

   Cui, Tiangang, Dolgov, Sergey, and Scheichl, Robert

   SIAM Journal on Scientific Computing, C1–C29, 2024 DOI arXiv
2. IP

   Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems

   Cui, Tiangang, Detommaso, Gianluca, and Scheichl, Robert

   Inverse Problems, 035005, 2024 DOI arXiv
3. JMLR

   Tensor-train methods for sequential state and parameter learning in state-space models

   Zhao, Yiran, and Cui, Tiangang

   Journal of Machine Learning Research, 25, 1–51, 2024 arXiv
4. JSC

   Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems

   Cui, Tiangang, De Sterck, Hans, Gilbert, Alexander D, Polishchuk, Stanislav, and Scheichl, Robert

   Journal of Scientific Computing, 99, 1–34, 2024 arXiv

2023

1. CiCP

   A variational neural network approach for glacier modelling with nonlinear rheology

   Cui, Tiangang, Wang, Zhongjian, and Zhang, Zhiwen

   Communications in Computational Physics, 34, 934–954, 2023 DOI arXiv
2. JCP

   Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction

   Cui, Tiangang, Dolgov, Sergey, and Zahm, Olivier

   Journal of Computational Physics, 112103, 2023 DOI arXiv

2022

1. Bernoulli

   A unified performance analysis of likelihood-informed subspace methods

   Cui, Tiangang, and Tong, Xin T

   Bernoulli, 28, 2788–2815, 2022 DOI arXiv
2. MathComp

   Certified dimension reduction in nonlinear Bayesian inverse problems

   Zahm, Olivier, Cui, Tiangang, Law, Kody, Spantini, Alessio, and Marzouk, Youssef

   Mathematics of Computation, 91, 1789–1835, 2022 DOI arXiv
3. IP

   Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems

   Cui, Tiangang, Tong, Xin T, and Zahm, Olivier

   Inverse Problems, 38, 124002, 2022 DOI arXiv
4. FoCM

   Deep composition of tensor trains using squared inverse Rosenblatt transports

   Cui, Tiangang, and Dolgov, Sergey

   Foundations of Computational Mathematics, 22, 1863–1922, 2022 DOI arXiv

2021

1. IP

   Data-free likelihood-informed dimension reduction of Bayesian inverse problems

   Cui, Tiangang, and Zahm, Olivier

   Inverse Problems, 37, 045009, 2021 DOI arXiv
2. JUQ

   Optimization-based Markov chain Monte Carlo methods for nonlinear hierarchical statistical inverse problems

   Bardsley, Johnathan M, and Cui, Tiangang

   SIAM/ASA Journal on Uncertainty Quantification, 9, 29–64, 2021 DOI arXiv
3. NeuroImage

   Identification of community structure-based brain states and transitions using functional MRI

   Bian, Lingbin, Cui, Tiangang, Yeo, BT Thomas, Fornito, Alex, Razi, Adeel, and Keith, Jonathan

   NeuroImage, 244, 118635, 2021 DOI arXiv

2020

1. IP

   Semivariogram methods for modeling Whittle–Matérn priors in Bayesian inverse problems

   Brown, Richard D, Bardsley, Johnathan M, and Cui, Tiangang

   Inverse Problems, 36, 055006, 2020 DOI arXiv
2. SISC

   Scalable optimization-based sampling on function space

   Bardsley, Johnathan M, Cui, Tiangang, Marzouk, Youssef M, and Wang, Zheng

   SIAM Journal on Scientific Computing, 42, A1317–A1347, 2020 DOI arXiv
3. PeerJ

   A non-linear reverse-engineering method for inferring genetic regulatory networks

   Wu, Siyuan, Cui, Tiangang, Zhang, Xinan, and Tian, Tianhai

   PeerJ, 8, e9065, 2020
4. GEM

   Randomized reduced forward models for efficient Metropolis–Hastings MCMC, with application to subsurface fluid flow and capacitance tomography

   Fox, Colin, Cui, Tiangang, and Neumayer, Markus

   GEM-International Journal on Geomathematics, 11, 1–38, 2020 DOI arXiv

2019

1. IJNME

   A posteriori stochastic correction of reduced models in delayed-acceptance MCMC, with application to multiphase subsurface inverse problems

   Cui, Tiangang, Fox, Colin, and O’Sullivan, Michael J

   International Journal for Numerical Methods in Engineering, 118, 578–605, 2019 DOI arXiv
2. IJUQ

   Using parallel Markov chain Monte Carlo to quantify uncertainties in geothermal reservoir calibration

   Cui, Tiangang, Fox, Colin, O’Sullivan, Mike, and Nicholls, Geoff

   International Journal for Uncertainty Quantification, 2019 DOI
3. J. Struct. Geol.

   Extraction of high-resolution structural orientations from digital data: A Bayesian approach

   Thiele, Samuel T, Grose, Lachlan, Cui, Tiangang, Cruden, Alexander R, and Micklethwaite, Steven

   Journal of Structural Geology, 122, 106–115, 2019 DOI

2018

1. J. Struct. Biol

   Rapid near-atomic resolution single-particle 3D reconstruction with SIMPLE

   Reboul, Cyril F, Kiesewetter, Simon, Eager, Michael, Belousoff, Matthew, Cui, Tiangang, De Sterck, Hans, Elmlund, Dominika, and Elmlund, Hans

   Journal of structural biology, 204, 172–181, 2018 DOI

2017

1. SISC

   Goal-oriented optimal approximations of Bayesian linear inverse problems

   Spantini, Alessio, Cui, Tiangang, Willcox, Karen, Tenorio, Luis, and Marzouk, Youssef

   SIAM Journal on Scientific Computing, 39, S167–S196, 2017 DOI arXiv
2. SISC

   Bayesian inverse problems with l_1 priors: a randomize-then-optimize approach

   Wang, Zheng, Bardsley, Johnathan M, Solonen, Antti, Cui, Tiangang, and Marzouk, Youssef M

   SIAM Journal on Scientific Computing, 39, S140–S166, 2017 DOI arXiv

2016

1. JCP

   Dimension-independent likelihood-informed MCMC

   Cui, Tiangang, Law, Kody JH, and Marzouk, Youssef M

   Journal of Computational Physics, 304, 109–137, 2016 DOI arXiv
2. JHE

   Pragmatic approach to calibrating distributed parameter groundwater models from pumping test data using adaptive delayed acceptance MCMC

   Cui, Tiangang, Ward, Nicholas Dudley, Eveson, Simon, and Lähivaara, Timo

   Journal of Hydrologic Engineering, 21, 06015011, 2016
3. IP

   On dimension reduction in Gaussian filters

   Solonen, Antti, Cui, Tiangang, Hakkarainen, Janne, and Marzouk, Youssef

   Inverse Problems, 32, 045003, 2016 DOI arXiv
4. JCP

   Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

   Cui, Tiangang, Marzouk, Youssef M, and Willcox, Karen E

   Journal of Computational Physics, 315, 363–387, 2016 DOI arXiv
5. CMAME

   Multifidelity importance sampling

   Peherstorfer, Benjamin, Cui, Tiangang, Marzouk, Youssef, and Willcox, Karen

   Computer Methods in Applied Mechanics and Engineering, 300, 490–509, 2016 DOI

2015

1. SISC

   Optimal low-rank approximations of Bayesian linear inverse problems

   Spantini, Alessio, Solonen, Antti, Cui, Tiangang, Martin, James, Tenorio, Luis, and Marzouk, Youssef

   SIAM Journal on Scientific Computing, 37, A2451–A2487, 2015 DOI arXiv
2. IJNME

   Data-driven model reduction for the Bayesian solution of inverse problems

   Cui, Tiangang, Marzouk, Youssef M, and Willcox, Karen E

   International Journal for Numerical Methods in Engineering, 102, 966–990, 2015 DOI arXiv

2014

1. JHE

   Characterization of parameters for a spatially heterogenous aquifer from pumping test data

   Cui, Tiangang, Dudley Ward, Nicholas, and Kaipio, Jari

   Journal of Hydrologic Engineering, 19, 1203–1213, 2014
2. IP

   Likelihood-informed dimension reduction for nonlinear inverse problems

   Cui, Tiangang, Martin, James, Marzouk, Youssef M, Solonen, Antti, and Spantini, Alessio

   Inverse Problems, 30, 114015, 2014 DOI arXiv

2013

1. JHE

   Uncertainty quantification for stream depletion tests

   Cui, Tiangang, and Ward, Nicholas Dudley

   Journal of Hydrologic Engineering, 18, 1581–1590, 2013

2011

1. WRR

   Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm

   Cui, T, Fox, C, and O’sullivan, MJ

   Water Resources Research, 47, 2011 DOI

2019

1. Optimization methods for inverse problems

   Ye, Nan, Roosta-Khorasani, Farbod, and Cui, Tiangang

   121–140, 2019 DOI
2. A Metropolis-Hastings-within-Gibbs sampler for nonlinear hierarchical-Bayesian inverse problems

   Bardsley, Johnathan M, and Cui, Tiangang

   3–12, 2019 DOI

2018

1. NIPS

   A Stein variational Newton method

   Detommaso, Gianluca, Cui, Tiangang, Marzouk, Youssef, Spantini, Alessio, and Scheichl, Robert

   In Advances in Neural Information Processing Systems 9169–9179, 2018 arXiv
2. IEEE

   Mathematical modelling of genetic network for regulating the fate determination of hematopoietic stem cells

   Wu, Siyuan, Cui, Tiangang, and Tian, Tianhai

   In 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) 2167–2173, 2018
3. MCQMC

   Network Structure Change Point Detection by Posterior Predictive Discrepancy

   Bian, Lingbin, Cui, Tiangang, Sofronov, Georgy, and Keith, Jonathan

   In International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing 107–123, 2018

1. arxiv

   l_∞-approximation of localized distributions

   Cui, Tiangang, Liu, Shuigen, and Tong, Xin

   2024 arXiv
2. arxiv

   Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds

   Cui, Tiangang, and Gorodetsky, Alex

   2024 arXiv
3. arxiv

   A tensor-train reduced basis solver for parameterized partial differential equations

   Mueller, Nicholas, Zhao, Yiran, Badia, Santiago, and Cui, Tiangang

   2024 arXiv
4. arxiv

   Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities

   Li, Matthew TC, Cui, Tiangang, Li, Fengyi, Marzouk, Youssef, and Zahm, Olivier

   2024 arXiv
5. arxiv

   Optimal Riemannian metric for Poincar {\backslash’e} inequalities and how to ideally precondition Langevin dymanics

   Cui, Tiangang, Tong, Xin, and Zahm, Olivier

   2024 arXiv
6. arxiv

   Sequential transport maps using SoS density estimation and $\backslashalpha $-divergences

   Zanger, Benjamin, Zahm, Olivier, Cui, Tiangang, and Schreiber, Martin

   2024 arXiv

1. arxiv

   Self-reinforced polynomial approximation methods for concentrated probability densities

   Cui, Tiangang, Dolgov, Sergey, and Zahm, Olivier

   2023 arXiv

1. arxiv

   Stein variational online changepoint detection with applications to Hawkes processes and neural networks

   Detommaso, Gianluca, Hoitzing, Hanne, Cui, Tiangang, and Alamir, Ardavan

   2019 arXiv