186 citations · 711 across the 31 of their papers we have counts for
32 papers
Bernstein approximation and beyond: proofs by means of elementary probability theory
Tiangang Cui, Friedrich Pillichshammer
Bernstein polynomials provide a constructive proof for the Weierstrass approximation theorem, which states that every continuous function on a closed bounded interval can be unifor…
Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation
Tiangang Cui, Josef Dick, Friedrich Pillichshammer
We study numerical integration over bounded regions in with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, wh…
Self-reinforced polynomial approximation methods for concentrated probability densities
Tiangang Cui, Sergey Dolgov, Olivier Zahm
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible tran…
Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems
Tiangang Cui, Hans De Sterck, Alexander D. Gilbert +2
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients.…
Tensor-train methods for sequential state and parameter learning in state-space models
Yiran Zhao, Tiangang Cui
We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor train (TT) deco…
A variational neural network approach for glacier modelling with nonlinear rheology
Tiangang Cui, Zhongjian Wang, Zhiwen Zhang
In this paper, we propose a mesh-free method to solve full stokes equation which models the glacier movement with nonlinear rheology. Our approach is inspired by the Deep-Ritz meth…