Dr Tiangang Cui

Research Overview

With backgrounds in applied mathematics and engineering, my research interest lies in the algorithmic interface between computational mathematics and data science, with a specific focus on integrating data-driven learning and mathematical models for issuing credible model-based predictions and decisions. I develop scalable statistical inference tools for computational inverse problems and uncertainty quantification. I also develop multilevel methods and model reduction methods that enable the deployment of statistical learning algorithms in large-scale real-world applications such as subsurface flows and geophysics.

Selected Publications

[1] Cui, Tiangang ; Fox, Colin ; O'Sullivan, Michael J. "A posteriori stochastic correction of reduced models in delayed-acceptance MCMC, with application to multiphase subsurface inverse problems". In: International Journal for Numerical Methods in Engineering. 2019 ; Vol. 118, No. 10. pp. 578-605. https://doi.org/10.1002/nme.6028

[2] Cui, Tiangang ; Law, Kody J H ; Marzouk, Youssef M. "Dimension-independent likelihood-informed MCMC". In: Journal of Computational Physics. 2016 ; Vol. 304. pp. 109-137. https://doi.org/10.1016/j.jcp.2015.10.008

[3] Cui, Tiangang ; Marzouk, Youssef ; Willcox, Karen. "Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction". In: Journal of Computational Physics. 2016 ; Vol. 315. pp. 363-387. https://doi.org/10.1016/j.jcp.2016.03.055

[4] Cui, Tiangang ; Marzouk, Youssef M. ; Willcox, Karen E. "Data-driven model reduction for the Bayesian solution of inverse problems". In: International Journal for Numerical Methods in Engineering. 2015 ; Vol. 102, No. 5. pp. 966-990. https://doi.org/10.1002/nme.4748

[5] Cui, T. ; Martin, J. ; Marzouk, Y. M. ; Solonen, A. ; Spantini, A. "Likelihood-informed dimension reduction for nonlinear inverse problems". In: Inverse Problems. 2014 ; Vol. 30, No. 11. https://doi.org/10.1088/0266-5611/30/11/114015