Solving parametric PDE problems with artificial neural networks

dc.contributor.author

Khoo, Y

dc.contributor.author

Lu, J

dc.contributor.author

Ying, L

dc.date.accessioned

2017-11-30T22:00:41Z

dc.date.available

2017-11-30T22:00:41Z

dc.date.issued

2017-11-30

dc.description.abstract

The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often the variability of physical quantities derived from PDE can be captured by a few features on the space of random coefficients. Based on such observation, we propose using neural-network, a technique gaining prominence in machine learning tasks, to parameterize the physical quantity of interest as a function of random input coefficients. The simplicity and accuracy of the approach are demonstrated through notable examples of PDEs in engineering and physics.

dc.format.extent

12 pages, 5 figures, 2 tables

dc.identifier

http://arxiv.org/abs/1707.03351v2

dc.identifier.uri

https://hdl.handle.net/10161/15784

dc.publisher

Cambridge University Press (CUP)

dc.subject

math.NA

dc.subject

math.NA

dc.subject

65Nxx

dc.title

Solving parametric PDE problems with artificial neural networks

dc.type

Journal article

duke.contributor.orcid

Lu, J|0000-0001-6255-5165

pubs.author-url

http://arxiv.org/abs/1707.03351v2

pubs.organisational-group

Chemistry

pubs.organisational-group

Duke

pubs.organisational-group

Mathematics

pubs.organisational-group

Physics

pubs.organisational-group

Temp group - logins allowed

pubs.organisational-group

Trinity College of Arts & Sciences

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