Parallel Zolotarev-SVD for the analysis of rocket combustion data

Abstract

Singular value decomposition (SVD), also known as principal component analysis (PCA), is one of the oldest and most fundamental, but also very powerful mathematical tools in data science. This poster is concerned with the application of modern high-performance SVD algorithms to problems arising in, e.g., the context of rocket combustion at the German Aerospace Center (DLR). We report on our implementation within the PyTorch- and mpi4py-based HPC-data analytics software HEAT (Helmholtz Analytics Toolkit) developed at DLR, JSC, and KIT (Götz et al., 2020 IEEE International Conference on Big Data, pp. 276-287). The core of our SVD implementation is formed by the highly parallelizable Zolotarev-SVD algorithm proposed by Y. Nakatsukasa and R.W. Freund (2016, SIAM Review, Vol. 58, No. 3, pp. 461-493). We present numerical experiments on the respective scaling behavior. Moreover, depending on the concrete problem type, other well-known techniques, such as randomized or incremental algorithms, are shown to allow for further reduction of the computational costs.