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Operator compressio...
Operator compression with deep neural networks
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- Kröpfl, Fabian (author)
- Universität Augsburg,University of Augsburg
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- Maier, Roland, 1993 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik,Department of Mathematical Sciences, Applied Mathematics and Statistics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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- Peterseim, Daniel (author)
- Universität Augsburg,University of Augsburg
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(creator_code:org_t)
- 2021
- English.
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In: ArXiv Preprint 2105.12080.
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Deep learning
- neural networks
- numerical homogenization
- model order reduction
- model order reduction
Publication and Content Type
- vet (subject category)
- ovr (subject category)
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