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Learning to differe...
Learning to differentiate
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- Ålund, Oskar, 1987- (författare)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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- Iaccarino, Gianluca (författare)
- Stanford University, Stanford, United States of America
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten,University of Johannesburg, South Africa
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(creator_code:org_t)
- Elsevier, 2021
- 2021
- Engelska.
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 424
- Relaterad länk:
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Artificial neural networks together with associated computational libraries provide a powerful framework for constructing both classification and regression algorithms. In this paper we use neural networks to design linear and non-linear discrete differential operators. We show that neural network based operators can be used to construct stable discretizations of initial boundary-value problems by ensuring that the operators satisfy a discrete analogue of integration-by-parts known as summation-by-parts. Our neural network approach with linear activation functions is compared and contrasted with a more traditional linear algebra approach. An application to overlapping grids is explored. The strategy developed in this work opens the door for constructing stable differential operators on general meshes.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Neural networks
- Discrete differential operators
- Stability
- Summation-by-parts
- Overlapping grids
Publikations- och innehållstyp
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- art (ämneskategori)
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