Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics
. The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic...
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| Veröffentlicht in: | European physical journal plus 2018-05, Vol.133 (5), p.184, Article 184 |
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| creator | Ahmad, Iftikhar Ahmad, Sufyan Awais, Muhammad Ul Islam Ahmad, Siraj Asif Zahoor Raja, Muhammad |
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The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs. |
| doi_str_mv | 10.1140/epjp/i2018-12013-3 |
| format | Article |
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The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2018-12013-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Artificial intelligence ; Atomic ; Complex Systems ; Condensed Matter Physics ; Cost function ; Genetic algorithms ; Information technology ; Mathematical and Computational Physics ; Mathematical models ; Mathematics ; Molecular ; Neural networks ; Nonlinear optics ; Optical and Plasma Physics ; Optics ; Partial differential equations ; Physics ; Physics and Astronomy ; Quadratic programming ; Regular Article ; Statistical analysis ; Theoretical ; Variance analysis</subject><ispartof>European physical journal plus, 2018-05, Vol.133 (5), p.184, Article 184</ispartof><rights>Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-76005da77a36fbe26bf70f2b4d7a15bd1633a172ecc7ddfc74dde0d2e6369a123</citedby><cites>FETCH-LOGICAL-c319t-76005da77a36fbe26bf70f2b4d7a15bd1633a172ecc7ddfc74dde0d2e6369a123</cites><orcidid>0000-0001-9953-822X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/i2018-12013-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919492293?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Ahmad, Iftikhar</creatorcontrib><creatorcontrib>Ahmad, Sufyan</creatorcontrib><creatorcontrib>Awais, Muhammad</creatorcontrib><creatorcontrib>Ul Islam Ahmad, Siraj</creatorcontrib><creatorcontrib>Asif Zahoor Raja, Muhammad</creatorcontrib><title>Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.</description><subject>Applied and Technical Physics</subject><subject>Artificial intelligence</subject><subject>Atomic</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Cost function</subject><subject>Genetic algorithms</subject><subject>Information technology</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Molecular</subject><subject>Neural networks</subject><subject>Nonlinear optics</subject><subject>Optical and Plasma Physics</subject><subject>Optics</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quadratic programming</subject><subject>Regular Article</subject><subject>Statistical analysis</subject><subject>Theoretical</subject><subject>Variance analysis</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kMtKAzEUhoMoWGpfwFXAdWxunZilFC8DRQV1HTKTTEmZJtNkpuAj-Ry-mJlW0JVncS7w_-dwPgAuCb4mhOO57Tbd3FFMbhDJmSF2AiaUSIwWnPPTP_05mKW0wTm4JFzyCXh9skMMyO5DO_QueB0_YB22XR78GnY6auPWW9iECF-0863df31Cuxv0KEZlCZ2HPvjWeasjDF3v6nQBzhrdJjv7qVPwfn_3tnxEq-eHcnm7QjUjskeiwHhhtBCaFU1laVE1Aje04kZosqgMKRjTRFBb18KYphbcGIsNtQUrpCaUTcHVcW8Xw26wqVebMESfTyoqieSSUsmyih5VdQwpRduoLrpt_lMRrEZ-auSnDvzUgZ8aTexoSlns1zb-rv7H9Q0D_Xb9</recordid><startdate>20180501</startdate><enddate>20180501</enddate><creator>Ahmad, Iftikhar</creator><creator>Ahmad, Sufyan</creator><creator>Awais, Muhammad</creator><creator>Ul Islam Ahmad, Siraj</creator><creator>Asif Zahoor Raja, Muhammad</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0001-9953-822X</orcidid></search><sort><creationdate>20180501</creationdate><title>Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics</title><author>Ahmad, Iftikhar ; Ahmad, Sufyan ; Awais, Muhammad ; Ul Islam Ahmad, Siraj ; Asif Zahoor Raja, Muhammad</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-76005da77a36fbe26bf70f2b4d7a15bd1633a172ecc7ddfc74dde0d2e6369a123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applied and Technical Physics</topic><topic>Artificial intelligence</topic><topic>Atomic</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Cost function</topic><topic>Genetic algorithms</topic><topic>Information technology</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Molecular</topic><topic>Neural networks</topic><topic>Nonlinear optics</topic><topic>Optical and Plasma Physics</topic><topic>Optics</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quadratic programming</topic><topic>Regular Article</topic><topic>Statistical analysis</topic><topic>Theoretical</topic><topic>Variance analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ahmad, Iftikhar</creatorcontrib><creatorcontrib>Ahmad, Sufyan</creatorcontrib><creatorcontrib>Awais, Muhammad</creatorcontrib><creatorcontrib>Ul Islam Ahmad, Siraj</creatorcontrib><creatorcontrib>Asif Zahoor Raja, Muhammad</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ahmad, Iftikhar</au><au>Ahmad, Sufyan</au><au>Awais, Muhammad</au><au>Ul Islam Ahmad, Siraj</au><au>Asif Zahoor Raja, Muhammad</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2018-05-01</date><risdate>2018</risdate><volume>133</volume><issue>5</issue><spage>184</spage><pages>184-</pages><artnum>184</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>.
The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2018-12013-3</doi><orcidid>https://orcid.org/0000-0001-9953-822X</orcidid></addata></record> |
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| subjects | Applied and Technical Physics Artificial intelligence Atomic Complex Systems Condensed Matter Physics Cost function Genetic algorithms Information technology Mathematical and Computational Physics Mathematical models Mathematics Molecular Neural networks Nonlinear optics Optical and Plasma Physics Optics Partial differential equations Physics Physics and Astronomy Quadratic programming Regular Article Statistical analysis Theoretical Variance analysis |
| title | Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics |
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