Parallelization of low-rank tensor methods
Title: Parallelization of low-rank tensor methods
SNIC Project: SNIC 2021/22-561
Project Type: SNIC Small Compute
Principal Investigator: Katharina Kormann <>
Affiliation: Uppsala universitet
Duration: 2021-08-23 – 2022-09-01
Classification: 10105


Low-rank tensor methods have shown to be very efficient in compressing high-dimensional data. In earlier research, we have developed a low-rank tensor solution of the Vlasov equation in six-dimensional phase space. While the algorithm shows very efficient performance on simple benchmark problems, parallelization is necessary to solve more complex problems. This project has the aim of developing a shared-memory parallelization of the hierarchical Tucker method, a particular low-rank tensor format. Since low-rank tensor compression relies on matrix decompositions, they are rather hard to parallelize over several nodes. We are therefore planing to develop a shared memory parallel version both for CPU and GPU. The challenging part is to handle adaptive ranks in the hierarchical Tucker decomposition which implies changing size of the required memory. On the other hand, we already have a MPI-parallel version of a hierarchical Tucker solution of the Vlasov equation which only uses the compression on parts of the dimensions and parallelizes along the other dimensions. Benchmark runs for this version will be run on the CPU nodes.