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Learning to differe...
Learning to differentiate
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- Ålund, Oskar, 1987- (author)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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- Iaccarino, Gianluca (author)
- Stanford University, Stanford, United States of America
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- Nordström, Jan, 1953- (author)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten,University of Johannesburg, South Africa
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(creator_code:org_t)
- Elsevier, 2021
- 2021
- English.
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In: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 424
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Neural networks
- Discrete differential operators
- Stability
- Summation-by-parts
- Overlapping grids
Publication and Content Type
- ref (subject category)
- art (subject category)
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