Speaker
Description
We consider a new approach to low-rank approximation of solutions to parameter -dependent PDEs that combines a representation in hierarchical tensor format with sparse polynomial expansions. We construct a low-rank adaptive Galerkin method for parametric elliptic problems that uses a tensor soft thresholding operation for rank reduction and discretization refinement based on lower-dimensional projected quantities. Unlike existing adaptive low-rank schemes, we obtain near-optimal ranks and discretizations without coarsening the iterates. In particular, for parametric problems with an anisotropic dependence on many variables, the new method leads to improved performance compared to existing adaptive tensor approximations that separate all variables into different tensor modes. Numerical experiments illustrate the effectiveness of the scheme.
