Harmonic (Quantum) Neural Networks
Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of firs...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2023-08 |
|---|---|
| Hauptverfasser: | , , , , , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Ghosh, Atiyo Gentile, Antonio A Dagrada, Mario Lee, Chul Kim, Seong-Hyok Cha, Hyukgeun Choi, Yunjun Kim, Brad Jeong-Il Kye Elfving, Vincent E |
| description | Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance. |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2754997990</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2754997990</sourcerecordid><originalsourceid>FETCH-proquest_journals_27549979903</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mRQ8kgsys3Py0xW0AgsTcwrKc3VVPBLLS1KzAFSJeX5RdnFPAysaYk5xam8UJqbQdnNNcTZQ7egKL-wNLW4JD4rv7QoDygVb2RuamJpaW5paWBMnCoAPvYtsg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2754997990</pqid></control><display><type>article</type><title>Harmonic (Quantum) Neural Networks</title><source>Free E- Journals</source><creator>Ghosh, Atiyo ; Gentile, Antonio A ; Dagrada, Mario ; Lee, Chul ; Kim, Seong-Hyok ; Cha, Hyukgeun ; Choi, Yunjun ; Kim, Brad ; Jeong-Il Kye ; Elfving, Vincent E</creator><creatorcontrib>Ghosh, Atiyo ; Gentile, Antonio A ; Dagrada, Mario ; Lee, Chul ; Kim, Seong-Hyok ; Cha, Hyukgeun ; Choi, Yunjun ; Kim, Brad ; Jeong-Il Kye ; Elfving, Vincent E</creatorcontrib><description>Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Computer architecture ; Divergence ; Domain decomposition methods ; Electrostatics ; Harmonic functions ; Inverse problems ; Machine learning ; Mathematical analysis ; Neural networks ; Optimization ; Path planning ; Quantum computing ; Random walk ; Wave equations</subject><ispartof>arXiv.org, 2023-08</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Ghosh, Atiyo</creatorcontrib><creatorcontrib>Gentile, Antonio A</creatorcontrib><creatorcontrib>Dagrada, Mario</creatorcontrib><creatorcontrib>Lee, Chul</creatorcontrib><creatorcontrib>Kim, Seong-Hyok</creatorcontrib><creatorcontrib>Cha, Hyukgeun</creatorcontrib><creatorcontrib>Choi, Yunjun</creatorcontrib><creatorcontrib>Kim, Brad</creatorcontrib><creatorcontrib>Jeong-Il Kye</creatorcontrib><creatorcontrib>Elfving, Vincent E</creatorcontrib><title>Harmonic (Quantum) Neural Networks</title><title>arXiv.org</title><description>Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.</description><subject>Algorithms</subject><subject>Computer architecture</subject><subject>Divergence</subject><subject>Domain decomposition methods</subject><subject>Electrostatics</subject><subject>Harmonic functions</subject><subject>Inverse problems</subject><subject>Machine learning</subject><subject>Mathematical analysis</subject><subject>Neural networks</subject><subject>Optimization</subject><subject>Path planning</subject><subject>Quantum computing</subject><subject>Random walk</subject><subject>Wave equations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mRQ8kgsys3Py0xW0AgsTcwrKc3VVPBLLS1KzAFSJeX5RdnFPAysaYk5xam8UJqbQdnNNcTZQ7egKL-wNLW4JD4rv7QoDygVb2RuamJpaW5paWBMnCoAPvYtsg</recordid><startdate>20230813</startdate><enddate>20230813</enddate><creator>Ghosh, Atiyo</creator><creator>Gentile, Antonio A</creator><creator>Dagrada, Mario</creator><creator>Lee, Chul</creator><creator>Kim, Seong-Hyok</creator><creator>Cha, Hyukgeun</creator><creator>Choi, Yunjun</creator><creator>Kim, Brad</creator><creator>Jeong-Il Kye</creator><creator>Elfving, Vincent E</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20230813</creationdate><title>Harmonic (Quantum) Neural Networks</title><author>Ghosh, Atiyo ; Gentile, Antonio A ; Dagrada, Mario ; Lee, Chul ; Kim, Seong-Hyok ; Cha, Hyukgeun ; Choi, Yunjun ; Kim, Brad ; Jeong-Il Kye ; Elfving, Vincent E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_27549979903</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Computer architecture</topic><topic>Divergence</topic><topic>Domain decomposition methods</topic><topic>Electrostatics</topic><topic>Harmonic functions</topic><topic>Inverse problems</topic><topic>Machine learning</topic><topic>Mathematical analysis</topic><topic>Neural networks</topic><topic>Optimization</topic><topic>Path planning</topic><topic>Quantum computing</topic><topic>Random walk</topic><topic>Wave equations</topic><toplevel>online_resources</toplevel><creatorcontrib>Ghosh, Atiyo</creatorcontrib><creatorcontrib>Gentile, Antonio A</creatorcontrib><creatorcontrib>Dagrada, Mario</creatorcontrib><creatorcontrib>Lee, Chul</creatorcontrib><creatorcontrib>Kim, Seong-Hyok</creatorcontrib><creatorcontrib>Cha, Hyukgeun</creatorcontrib><creatorcontrib>Choi, Yunjun</creatorcontrib><creatorcontrib>Kim, Brad</creatorcontrib><creatorcontrib>Jeong-Il Kye</creatorcontrib><creatorcontrib>Elfving, Vincent E</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ghosh, Atiyo</au><au>Gentile, Antonio A</au><au>Dagrada, Mario</au><au>Lee, Chul</au><au>Kim, Seong-Hyok</au><au>Cha, Hyukgeun</au><au>Choi, Yunjun</au><au>Kim, Brad</au><au>Jeong-Il Kye</au><au>Elfving, Vincent E</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Harmonic (Quantum) Neural Networks</atitle><jtitle>arXiv.org</jtitle><date>2023-08-13</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2023-08 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_2754997990 |
| source | Free E- Journals |
| subjects | Algorithms Computer architecture Divergence Domain decomposition methods Electrostatics Harmonic functions Inverse problems Machine learning Mathematical analysis Neural networks Optimization Path planning Quantum computing Random walk Wave equations |
| title | Harmonic (Quantum) Neural Networks |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T18%3A19%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Harmonic%20(Quantum)%20Neural%20Networks&rft.jtitle=arXiv.org&rft.au=Ghosh,%20Atiyo&rft.date=2023-08-13&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2754997990%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2754997990&rft_id=info:pmid/&rfr_iscdi=true |