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dc.contributor.author
De Ryck, Tim
dc.contributor.supervisor
Mishra, Siddhartha
dc.date.accessioned
2020-02-07T15:15:39Z
dc.date.available
2020-02-07T12:06:58Z
dc.date.available
2020-02-07T15:15:39Z
dc.date.issued
2020-01-31
dc.identifier.uri
http://hdl.handle.net/20.500.11850/397533
dc.identifier.doi
10.3929/ethz-b-000397533
dc.description.abstract
Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the stencil shifts of the ENO and ENO-SR interpolation procedures can be exactly obtained using a deep ReLU neural network. In addition, we construct and provide error bounds for ReLU neural networks that directly approximate the output of the ENO and ENO- SR interpolation procedures. This surprising fact enables the transfer of several desirable properties of the ENO procedure to deep neural networks, including its high-order accuracy at approximating Lipschitz functions. Numerical tests for the resulting neural networks show excellent performance for interpolating rough functions, data compression and approximating solutions of nonlinear conservation laws.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Numerical analysis
en_US
dc.subject
Interpolation
en_US
dc.subject
Deep learning
en_US
dc.subject
ENO reconstruction
en_US
dc.subject
ReLU
en_US
dc.title
On the Approximation of Rough Functions with Artificial Neural Networks
en_US
dc.type
Master Thesis
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.size
97 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
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ethz.publication.place
Zurich
en_US
ethz.publication.status
published
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ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03851 - Mishra, Siddhartha / Mishra, Siddhartha
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
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ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03851 - Mishra, Siddhartha / Mishra, Siddhartha
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
en_US
ethz.date.deposited
2020-02-07T12:07:09Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-02-07T15:15:50Z
ethz.rosetta.lastUpdated
2022-03-29T00:55:58Z
ethz.rosetta.versionExported
true
ethz.COinS
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