Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

• Published in: Journal of computational physics 2023-03, Vol.484
• Main Authors: De Pascuale, Sebastian, Allen, Kenneth, Green, David L., Lore, Jeremy D.
• Format: Article
• Language: English
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CUR matrix decomposition; Data compression; Dimensionality reduction; Low-rank matrix approximation; Scrape-off-layer; SOLPS-ITER
• ISSN: 0021-9991; 1090-2716

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10–2. In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.