16871

Streaming GPU Singular Value and Dynamic Mode Decompositions

Seth D. Pendergrass, J. Nathan Kutz, Steven L. Brunton
University of Washington, Computer Engineering
arXiv:1612.07875 [math.NA], (23 Dec 2016)

@article{pendergrass2016streaming,

   title={Streaming GPU Singular Value and Dynamic Mode Decompositions},

   author={Pendergrass, Seth D. and Kutz, J. Nathan and Brunton, Steven L.},

   year={2016},

   month={dec},

   archivePrefix={"arXiv"},

   primaryClass={math.NA}

}

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This work develops a parallelized algorithm to compute the dynamic mode decomposition (DMD) on a graphics processing unit using the streaming method of snapshots singular value decomposition. This allows the algorithm to operate efficiently on streaming data by avoiding redundant inner-products as new data becomes available. In addition, it is possible to leverage the native compressed format of many data streams, such as HD video and computational physics codes that are represented sparsely in the Fourier domain, to massively reduce data transfer from CPU to GPU and to enable sparse matrix multiplications. Taken together, these algorithms facilitate real-time streaming DMD on high-dimensional data streams. We demonstrate the proposed method on numerous high-dimensional data sets ranging from video background modeling to scientific computing applications, where DMD is becoming a mainstay algorithm. The computational framework is developed as an open-source library written in C++ with CUDA, and the algorithms may be generalized to include other DMD advances, such as compressed sensing DMD, multi resolution DMD, or DMD with control. Keywords: Singular value decomposition, dynamic mode decomposition, streaming computations, graphics processing unit, video background modeling, scientific computing.
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