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  • Kröpfl, Fabian, et al. (author)
  • Operator compression with deep neural networks
  • 2021
  • In: ArXiv Preprint 2105.12080.
  • Other publication (other academic/artistic)abstract
    • This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may vary on a large range of scales. Based on existing methods that compress such a multiscale operator to a finite-dimensional sparse surrogate model on a given target scale, we propose to directly approximate the coefficient-to-surrogate map with a neural network. We emulate local assembly structures of the surrogates and thus only require a moderately sized network that can be trained efficiently in an offline phase. This enables large compression ratios and the online computation of a surrogate based on simple forward passes through the network is substantially accelerated compared to classical numerical upscaling approaches. We apply the abstract framework to a family of prototypical second-order elliptic heterogeneous diffusion operators as a demonstrating example.
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Type of publication
other publication (1)
Type of content
other academic/artistic (1)
Author/Editor
Maier, Roland, 1993 (1)
Peterseim, Daniel (1)
Kröpfl, Fabian (1)
University
University of Gothenburg (1)
Chalmers University of Technology (1)
Language
English (1)
Research subject (UKÄ/SCB)
Natural sciences (1)
Year
2021 (1)

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