Low-rank Tensor Approximation in Multi-parametric and Stochastic PDEs
Litvinenko, Alexander (KAUST, UQ & ECRC Centers)
Matthies, Hermann (TU Braunschweig, Inst. of Scientific Computing)
Nouy, Anthony (Ecole Centrale Nantes)
Approximations of stochastic and multi-parametric differential equations may lead to extremely high dimensional problems that suffer from the so called curse of dimensionality. Computational tractability may be recovered by relying on adaptive low-rank/sparse approximation. The tasks are 1) to keep a low-rank approximation of the high-dimensional input data through the whole computing process, 2) compute the solution and perform a post-processing in a low-rank tensor format. The post-processing may include computation of different statistics, visualization of a small portion of large data, large data analysis. The aim is to develop numerical methods which will reduce the computational cost as well as the storage requirement from O(n^d) to O(knd), where k is a small integer (related with the rank).
The purpose of this minisymposium is to bring together experts in adaptive discretization/solution of stochastic/multi-parametric problems, experts in multi-linear algebra and experts in uncertainty quantification methods.
Additionally, Alexander will give:
"Approximating Stochastic Galerkin Operator in the Tensor Train data format"
2) and present a poster
"Computation of Electromagnetic Fields Scattered From Dielectric Objects of Uncertain Shapes Using MLMC", joint work with Abdul-Lateef Haji-Ali, Ismail Enes Uysal, Huseyin Arda Ulku, Jesper Oppelstrup, Raul Tempone, and Hakan Bagcı.