Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier–Stokes equations
In this paper, we study the weak adversarial network (WAN) (Zang et al. in J Comput Phys 411:109409, 2020) method for solving Navier–Stokes (NS) equation numerically, including both forward and inverse problems. Firstly, the NS equation is converted to the biharmonic formulation leveraging the strea...
Gespeichert in:
| Veröffentlicht in: | Computational & applied mathematics 2024-02, Vol.43 (1), Article 61 |
|---|---|
| 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 | 1 |
| container_start_page | |
| container_title | Computational & applied mathematics |
| container_volume | 43 |
| creator | Li, Wen-Ran Yang, Rong Yang, Xin-Guang |
| description | In this paper, we study the weak adversarial network (WAN) (Zang et al. in J Comput Phys 411:109409, 2020) method for solving Navier–Stokes (NS) equation numerically, including both forward and inverse problems. Firstly, the NS equation is converted to the biharmonic formulation leveraging the stream function, then the biharmonic formulation equation contributes to a test function as an operator. Furthermore, the underlying NS equation is discretized by using two neural networks based on weak formulation. Finally, numerical results for some experiments are presented, this method shows advantages of stability and accuracy compared with other algorithms, especially this method is useful for problems which have no strong solutions. |
| doi_str_mv | 10.1007/s40314-023-02574-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2917581711</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2917581711</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-671812464c877cc6753467cdfe263c5720a4d06b16550d96bf6cb98bd6944b8e3</originalsourceid><addsrcrecordid>eNp9kEtOwzAQhi0EEqVwAVaWWAf8ip0sUXlKFSwAsbQcx6nSpnHxpC3suAM35CQ4pBI7FtZ4Zr5_ZvQjdErJOSVEXYAgnIqEMB5fqkQi99CIZkQlhBO2j0aM8SzhkvBDdAQwJ4QrKsQIvb86s8Cm3LgAJtSmwa3rtj4sAFc-YPDNpm5n_X9rQolNW-K67WGHV8EXjVtCX9hh7Com1i9XwQHUsYsfzKZ24fvz66nzCwfYva1NV_sWjtFBZRpwJ7s4Ri8318-Tu2T6eHs_uZwmlinSJVLRjDIhhc2UslaqlAupbFk5JrlNFSNGlEQWVKYpKXNZVNIWeVaUMheiyBwfo7Nhbjz3be2g03O_Dm1cqVlOVZpRRWmk2EDZ4AGCq_Qq1EsTPjQlundYDw7r6LD-dVjLKOKDCCLczlz4G_2P6gcZ8oEz</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2917581711</pqid></control><display><type>article</type><title>Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier–Stokes equations</title><source>SpringerLink Journals</source><creator>Li, Wen-Ran ; Yang, Rong ; Yang, Xin-Guang</creator><creatorcontrib>Li, Wen-Ran ; Yang, Rong ; Yang, Xin-Guang</creatorcontrib><description>In this paper, we study the weak adversarial network (WAN) (Zang et al. in J Comput Phys 411:109409, 2020) method for solving Navier–Stokes (NS) equation numerically, including both forward and inverse problems. Firstly, the NS equation is converted to the biharmonic formulation leveraging the stream function, then the biharmonic formulation equation contributes to a test function as an operator. Furthermore, the underlying NS equation is discretized by using two neural networks based on weak formulation. Finally, numerical results for some experiments are presented, this method shows advantages of stability and accuracy compared with other algorithms, especially this method is useful for problems which have no strong solutions.</description><identifier>ISSN: 2238-3603</identifier><identifier>EISSN: 1807-0302</identifier><identifier>DOI: 10.1007/s40314-023-02574-6</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algorithms ; Applications of Mathematics ; Computational Mathematics and Numerical Analysis ; Fluid flow ; Inverse problems ; Mathematical Applications in Computer Science ; Mathematical Applications in the Physical Sciences ; Mathematics ; Mathematics and Statistics ; Navier-Stokes equations ; Neural networks ; Wide area networks</subject><ispartof>Computational & applied mathematics, 2024-02, Vol.43 (1), Article 61</ispartof><rights>The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-671812464c877cc6753467cdfe263c5720a4d06b16550d96bf6cb98bd6944b8e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40314-023-02574-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40314-023-02574-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Li, Wen-Ran</creatorcontrib><creatorcontrib>Yang, Rong</creatorcontrib><creatorcontrib>Yang, Xin-Guang</creatorcontrib><title>Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier–Stokes equations</title><title>Computational & applied mathematics</title><addtitle>Comp. Appl. Math</addtitle><description>In this paper, we study the weak adversarial network (WAN) (Zang et al. in J Comput Phys 411:109409, 2020) method for solving Navier–Stokes (NS) equation numerically, including both forward and inverse problems. Firstly, the NS equation is converted to the biharmonic formulation leveraging the stream function, then the biharmonic formulation equation contributes to a test function as an operator. Furthermore, the underlying NS equation is discretized by using two neural networks based on weak formulation. Finally, numerical results for some experiments are presented, this method shows advantages of stability and accuracy compared with other algorithms, especially this method is useful for problems which have no strong solutions.</description><subject>Algorithms</subject><subject>Applications of Mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Fluid flow</subject><subject>Inverse problems</subject><subject>Mathematical Applications in Computer Science</subject><subject>Mathematical Applications in the Physical Sciences</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Navier-Stokes equations</subject><subject>Neural networks</subject><subject>Wide area networks</subject><issn>2238-3603</issn><issn>1807-0302</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEtOwzAQhi0EEqVwAVaWWAf8ip0sUXlKFSwAsbQcx6nSpnHxpC3suAM35CQ4pBI7FtZ4Zr5_ZvQjdErJOSVEXYAgnIqEMB5fqkQi99CIZkQlhBO2j0aM8SzhkvBDdAQwJ4QrKsQIvb86s8Cm3LgAJtSmwa3rtj4sAFc-YPDNpm5n_X9rQolNW-K67WGHV8EXjVtCX9hh7Com1i9XwQHUsYsfzKZ24fvz66nzCwfYva1NV_sWjtFBZRpwJ7s4Ri8318-Tu2T6eHs_uZwmlinSJVLRjDIhhc2UslaqlAupbFk5JrlNFSNGlEQWVKYpKXNZVNIWeVaUMheiyBwfo7Nhbjz3be2g03O_Dm1cqVlOVZpRRWmk2EDZ4AGCq_Qq1EsTPjQlundYDw7r6LD-dVjLKOKDCCLczlz4G_2P6gcZ8oEz</recordid><startdate>20240201</startdate><enddate>20240201</enddate><creator>Li, Wen-Ran</creator><creator>Yang, Rong</creator><creator>Yang, Xin-Guang</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240201</creationdate><title>Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier–Stokes equations</title><author>Li, Wen-Ran ; Yang, Rong ; Yang, Xin-Guang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-671812464c877cc6753467cdfe263c5720a4d06b16550d96bf6cb98bd6944b8e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Applications of Mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Fluid flow</topic><topic>Inverse problems</topic><topic>Mathematical Applications in Computer Science</topic><topic>Mathematical Applications in the Physical Sciences</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Navier-Stokes equations</topic><topic>Neural networks</topic><topic>Wide area networks</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Wen-Ran</creatorcontrib><creatorcontrib>Yang, Rong</creatorcontrib><creatorcontrib>Yang, Xin-Guang</creatorcontrib><collection>CrossRef</collection><jtitle>Computational & applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Wen-Ran</au><au>Yang, Rong</au><au>Yang, Xin-Guang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier–Stokes equations</atitle><jtitle>Computational & applied mathematics</jtitle><stitle>Comp. Appl. Math</stitle><date>2024-02-01</date><risdate>2024</risdate><volume>43</volume><issue>1</issue><artnum>61</artnum><issn>2238-3603</issn><eissn>1807-0302</eissn><abstract>In this paper, we study the weak adversarial network (WAN) (Zang et al. in J Comput Phys 411:109409, 2020) method for solving Navier–Stokes (NS) equation numerically, including both forward and inverse problems. Firstly, the NS equation is converted to the biharmonic formulation leveraging the stream function, then the biharmonic formulation equation contributes to a test function as an operator. Furthermore, the underlying NS equation is discretized by using two neural networks based on weak formulation. Finally, numerical results for some experiments are presented, this method shows advantages of stability and accuracy compared with other algorithms, especially this method is useful for problems which have no strong solutions.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40314-023-02574-6</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2238-3603 |
| ispartof | Computational & applied mathematics, 2024-02, Vol.43 (1), Article 61 |
| issn | 2238-3603 1807-0302 |
| language | eng |
| recordid | cdi_proquest_journals_2917581711 |
| source | SpringerLink Journals |
| subjects | Algorithms Applications of Mathematics Computational Mathematics and Numerical Analysis Fluid flow Inverse problems Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Navier-Stokes equations Neural networks Wide area networks |
| title | Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier–Stokes equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T07%3A57%3A41IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Weak%20adversarial%20networks%20for%20solving%20forward%20and%20inverse%20problems%20involving%202D%20incompressible%20Navier%E2%80%93Stokes%20equations&rft.jtitle=Computational%20&%20applied%20mathematics&rft.au=Li,%20Wen-Ran&rft.date=2024-02-01&rft.volume=43&rft.issue=1&rft.artnum=61&rft.issn=2238-3603&rft.eissn=1807-0302&rft_id=info:doi/10.1007/s40314-023-02574-6&rft_dat=%3Cproquest_cross%3E2917581711%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2917581711&rft_id=info:pmid/&rfr_iscdi=true |