A modified iterative PINN algorithm for strongly coupled system of boundary layer originated convection diffusion reaction problems in MHD flows with analysis
In this work, we design an iteration-based unsupervised neural network algorithm and the theoretical bound of the loss function through Barron space to solve reaction–convection–diffusion-based magnetohydrodynamic (MHD) coupled systems for 1D and 2D problems. Our algorithm is also be able to capture...
Gespeichert in:
| Veröffentlicht in: | Networks and heterogeneous media Jg. 20; H. 3; S. 1026 - 1060 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
AIMS Press
01.01.2025
|
| Schlagworte: | |
| ISSN: | 1556-1801 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In this work, we design an iteration-based unsupervised neural network algorithm and the theoretical bound of the loss function through Barron space to solve reaction–convection–diffusion-based magnetohydrodynamic (MHD) coupled systems for 1D and 2D problems. Our algorithm is also be able to capture the presence of boundary layers. In general, these systems are characterized by strong coupling in the reaction and convection processes and involve non-diagonally dominant matrices in the context of convection coupling. Traditional numerical techniques face challenges in approximating these problems due to the failure of the required maximum principle, which is used for the well-posedness and further convergence analysis of numerical solutions. We specifically provide a new modified iterative physics-informed neural network (MI-PINN)-based unsupervised deep learning algorithm to capture the layer behavior of singularly perturbed strongly coupled steady-state problems, appearing in MHD flows where theoretical analysis and numerical methods are limited. A different analysis based on the sigmoid activation function is provided for the steady-state case, which shows that the empirical loss under the $ L^2 $ norm is bounded and converges for the two layer-based networks- whenever the solution lies in the Barron space. Additionally, the proposed algorithm improves the neural network's output without using the boundary layer functions a priori and does not use hard constraints or interpolation with the neural network's solution. The experimental results show that the proposed algorithm performs very well for MHD flows appearing in the form of strongly coupled systems. |
|---|---|
| AbstractList | In this work, we design an iteration-based unsupervised neural network algorithm and the theoretical bound of the loss function through Barron space to solve reaction–convection–diffusion-based magnetohydrodynamic (MHD) coupled systems for 1D and 2D problems. Our algorithm is also be able to capture the presence of boundary layers. In general, these systems are characterized by strong coupling in the reaction and convection processes and involve non-diagonally dominant matrices in the context of convection coupling. Traditional numerical techniques face challenges in approximating these problems due to the failure of the required maximum principle, which is used for the well-posedness and further convergence analysis of numerical solutions. We specifically provide a new modified iterative physics-informed neural network (MI-PINN)-based unsupervised deep learning algorithm to capture the layer behavior of singularly perturbed strongly coupled steady-state problems, appearing in MHD flows where theoretical analysis and numerical methods are limited. A different analysis based on the sigmoid activation function is provided for the steady-state case, which shows that the empirical loss under the $ L^2 $ norm is bounded and converges for the two layer-based networks- whenever the solution lies in the Barron space. Additionally, the proposed algorithm improves the neural network's output without using the boundary layer functions a priori and does not use hard constraints or interpolation with the neural network's solution. The experimental results show that the proposed algorithm performs very well for MHD flows appearing in the form of strongly coupled systems. |
| Author | Kumar, Shridhar Patawari, Arihant Das, Pratibhamoy |
| Author_xml | – sequence: 1 givenname: Arihant surname: Patawari fullname: Patawari, Arihant – sequence: 2 givenname: Shridhar surname: Kumar fullname: Kumar, Shridhar – sequence: 3 givenname: Pratibhamoy surname: Das fullname: Das, Pratibhamoy |
| BookMark | eNo9UctOJCEUZeEkajsrf4C9aQeKKrpYGp-dqDOLcV25BZcWQ0EHaE39jN8qPW1mdW9OziMn55QchRiQkHPOLoUS7a_wOl02rOlY2x2RE951csl7xo_Jac5vjLVixcQJ-byiUzTOOjTUFUxQ3DvSP-vnZwp-E5MrrxO1MdFcUgwbP1Mdd1tf2XnOBScaLR3jLhhIM_UwY6JVtHEBSuXoGN5RFxcDrRl2l_dfQjhA2xRHj1OmLtCnhxtqffzI9KNGUgjg5-zyGflhwWf8-X0X5OXu9u_1w_Lx9_36-upxqRslyxKV7nknBHaSg8TGIsdaEGDVtr01WiqtpDBGgFJgNDDVKbNC2WODUksQC7I--JoIb8M2uan2GSK44R8Q02aAVJz2OCA2oEeFthdNa5lQvFdGjkaMKyN4jVmQi4OXTjHnhPa_H2fDfpqhTjN8TyO-ADpFimg |
| Cites_doi | 10.1007/BF02551274 10.1016/S0168-9274(97)00106-2 10.1016/j.apnum.2024.09.020 10.1016/j.jcp.2010.08.034 10.1002/zamm.201000153 10.1016/j.jcp.2018.10.045 10.1016/S0377-0427(00)00260-0 10.1016/j.cma.2022.115616 10.1093/imanum/drac085 10.1016/j.cam.2024.116223 10.1016/j.apnum.2019.07.003 10.1016/j.apnum.2023.10.003 10.1090/gsm/075 10.1016/j.jfranklin.2019.12.013 10.4208/cicp.OA-2020-0193 10.1007/s10444-019-09669-x 10.1016/j.apnum.2023.01.003 10.1007/s11071-015-1894-7 10.1016/j.jcp.2023.112702 10.1007/s00607-006-0215-x 10.1002/fld.5294 10.1007/s10546-021-00666-6 10.1007/s10915-022-01939-z 10.1016/j.jcp.2022.111768 10.1093/imanum/drab093 10.1016/j.jcp.2019.109136 10.1016/j.cnsns.2025.108627 10.1080/02331934.2025.2534119 10.1016/j.cam.2017.11.026 10.1109/18.256500 10.1016/S0096-3003(01)00291-0 10.1016/j.apnum.2022.09.012 10.1109/TSMC.2022.3152505 10.4208/ijnam2025-1020 10.1080/00036811.2024.2302405 10.1111/sapm.12763 10.2478/cmam-2009-0010 10.1016/j.bulsci.2025.103637 10.1007/s00365-021-09549-y 10.1007/s10483-024-3149-8 10.1016/j.cma.2020.113547 10.1007/s10444-007-9058-z 10.3934/nhm.2024048 10.1016/j.apnum.2019.08.028 10.1145/3689037 10.1016/j.aml.2012.02.018 10.1051/proc/202373048 |
| ContentType | Journal Article |
| CorporateAuthor | Department of Mathematics, Indian Institute of Technology Patna, India School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, India |
| CorporateAuthor_xml | – name: School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, India – name: Department of Mathematics, Indian Institute of Technology Patna, India |
| DBID | AAYXX CITATION DOA |
| DOI | 10.3934/nhm.2025045 |
| DatabaseName | CrossRef Directory of Open Access Journals (DOAJ) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EndPage | 1060 |
| ExternalDocumentID | oai_doaj_org_article_ee2acb9ef8324f039189d6bd3b7d3196 10_3934_nhm_2025045 |
| GroupedDBID | .4S .DC 123 AAYXX AENEX ALMA_UNASSIGNED_HOLDINGS AMVHM ARCSS CITATION DU5 E3Z EBS EJD GROUPED_DOAJ J9A RAN TUS |
| ID | FETCH-LOGICAL-c296t-e9c81533e561a6e2fe1e437aa7448fdc69c963dd3a99adca0959d7e68e2e6c6a3 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001587183400004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1556-1801 |
| IngestDate | Mon Nov 03 22:05:41 EST 2025 Sat Nov 29 07:26:43 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c296t-e9c81533e561a6e2fe1e437aa7448fdc69c963dd3a99adca0959d7e68e2e6c6a3 |
| OpenAccessLink | https://doaj.org/article/ee2acb9ef8324f039189d6bd3b7d3196 |
| PageCount | 35 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_ee2acb9ef8324f039189d6bd3b7d3196 crossref_primary_10_3934_nhm_2025045 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-01-01 |
| PublicationDateYYYYMMDD | 2025-01-01 |
| PublicationDate_xml | – month: 01 year: 2025 text: 2025-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Networks and heterogeneous media |
| PublicationYear | 2025 |
| Publisher | AIMS Press |
| Publisher_xml | – name: AIMS Press |
| References | key-10.3934/nhm.2025045-9 key-10.3934/nhm.2025045-7 key-10.3934/nhm.2025045-8 key-10.3934/nhm.2025045-5 key-10.3934/nhm.2025045-41 key-10.3934/nhm.2025045-6 key-10.3934/nhm.2025045-42 key-10.3934/nhm.2025045-3 key-10.3934/nhm.2025045-43 key-10.3934/nhm.2025045-4 key-10.3934/nhm.2025045-44 key-10.3934/nhm.2025045-1 key-10.3934/nhm.2025045-2 key-10.3934/nhm.2025045-40 key-10.3934/nhm.2025045-38 key-10.3934/nhm.2025045-39 key-10.3934/nhm.2025045-34 key-10.3934/nhm.2025045-35 key-10.3934/nhm.2025045-36 key-10.3934/nhm.2025045-37 key-10.3934/nhm.2025045-52 key-10.3934/nhm.2025045-53 key-10.3934/nhm.2025045-10 key-10.3934/nhm.2025045-54 key-10.3934/nhm.2025045-11 key-10.3934/nhm.2025045-55 key-10.3934/nhm.2025045-50 key-10.3934/nhm.2025045-51 key-10.3934/nhm.2025045-49 key-10.3934/nhm.2025045-45 key-10.3934/nhm.2025045-46 key-10.3934/nhm.2025045-47 key-10.3934/nhm.2025045-48 key-10.3934/nhm.2025045-63 key-10.3934/nhm.2025045-20 key-10.3934/nhm.2025045-64 key-10.3934/nhm.2025045-21 key-10.3934/nhm.2025045-65 key-10.3934/nhm.2025045-22 key-10.3934/nhm.2025045-66 key-10.3934/nhm.2025045-60 key-10.3934/nhm.2025045-61 key-10.3934/nhm.2025045-62 key-10.3934/nhm.2025045-16 key-10.3934/nhm.2025045-17 key-10.3934/nhm.2025045-18 key-10.3934/nhm.2025045-19 key-10.3934/nhm.2025045-12 key-10.3934/nhm.2025045-56 key-10.3934/nhm.2025045-13 key-10.3934/nhm.2025045-57 key-10.3934/nhm.2025045-14 key-10.3934/nhm.2025045-58 key-10.3934/nhm.2025045-15 key-10.3934/nhm.2025045-59 key-10.3934/nhm.2025045-30 key-10.3934/nhm.2025045-31 key-10.3934/nhm.2025045-32 key-10.3934/nhm.2025045-33 key-10.3934/nhm.2025045-27 key-10.3934/nhm.2025045-28 key-10.3934/nhm.2025045-29 key-10.3934/nhm.2025045-23 key-10.3934/nhm.2025045-67 key-10.3934/nhm.2025045-24 key-10.3934/nhm.2025045-25 key-10.3934/nhm.2025045-26 |
| References_xml | – ident: key-10.3934/nhm.2025045-50 – ident: key-10.3934/nhm.2025045-48 – ident: key-10.3934/nhm.2025045-35 doi: 10.1007/BF02551274 – ident: key-10.3934/nhm.2025045-5 – ident: key-10.3934/nhm.2025045-21 – ident: key-10.3934/nhm.2025045-31 – ident: key-10.3934/nhm.2025045-20 doi: 10.1016/S0168-9274(97)00106-2 – ident: key-10.3934/nhm.2025045-29 doi: 10.1016/j.apnum.2024.09.020 – ident: key-10.3934/nhm.2025045-63 – ident: key-10.3934/nhm.2025045-16 – ident: key-10.3934/nhm.2025045-8 doi: 10.1016/j.jcp.2010.08.034 – ident: key-10.3934/nhm.2025045-64 doi: 10.1002/zamm.201000153 – ident: key-10.3934/nhm.2025045-24 doi: 10.1016/j.jcp.2018.10.045 – ident: key-10.3934/nhm.2025045-58 doi: 10.1016/S0377-0427(00)00260-0 – ident: key-10.3934/nhm.2025045-26 doi: 10.1016/j.cma.2022.115616 – ident: key-10.3934/nhm.2025045-38 doi: 10.1093/imanum/drac085 – ident: key-10.3934/nhm.2025045-28 – ident: key-10.3934/nhm.2025045-40 doi: 10.1016/j.cam.2024.116223 – ident: key-10.3934/nhm.2025045-6 – ident: key-10.3934/nhm.2025045-30 – ident: key-10.3934/nhm.2025045-2 doi: 10.1016/j.apnum.2019.07.003 – ident: key-10.3934/nhm.2025045-12 doi: 10.1016/j.apnum.2023.10.003 – ident: key-10.3934/nhm.2025045-46 doi: 10.1090/gsm/075 – ident: key-10.3934/nhm.2025045-1 doi: 10.1016/j.jfranklin.2019.12.013 – ident: key-10.3934/nhm.2025045-41 – ident: key-10.3934/nhm.2025045-36 doi: 10.4208/cicp.OA-2020-0193 – ident: key-10.3934/nhm.2025045-13 doi: 10.1007/s10444-019-09669-x – ident: key-10.3934/nhm.2025045-53 doi: 10.1016/j.apnum.2023.01.003 – ident: key-10.3934/nhm.2025045-55 – ident: key-10.3934/nhm.2025045-59 – ident: key-10.3934/nhm.2025045-18 doi: 10.1007/s11071-015-1894-7 – ident: key-10.3934/nhm.2025045-27 doi: 10.1016/j.jcp.2023.112702 – ident: key-10.3934/nhm.2025045-56 doi: 10.1007/s00607-006-0215-x – ident: key-10.3934/nhm.2025045-7 – ident: key-10.3934/nhm.2025045-22 doi: 10.1002/fld.5294 – ident: key-10.3934/nhm.2025045-14 doi: 10.1007/s10546-021-00666-6 – ident: key-10.3934/nhm.2025045-65 – ident: key-10.3934/nhm.2025045-32 doi: 10.1007/s10915-022-01939-z – ident: key-10.3934/nhm.2025045-25 doi: 10.1016/j.jcp.2022.111768 – ident: key-10.3934/nhm.2025045-37 doi: 10.1093/imanum/drab093 – ident: key-10.3934/nhm.2025045-10 – ident: key-10.3934/nhm.2025045-39 doi: 10.1016/j.jcp.2019.109136 – ident: key-10.3934/nhm.2025045-42 – ident: key-10.3934/nhm.2025045-51 doi: 10.1016/j.cnsns.2025.108627 – ident: key-10.3934/nhm.2025045-61 doi: 10.1080/02331934.2025.2534119 – ident: key-10.3934/nhm.2025045-60 doi: 10.1016/j.cam.2017.11.026 – ident: key-10.3934/nhm.2025045-4 – ident: key-10.3934/nhm.2025045-66 doi: 10.1109/18.256500 – ident: key-10.3934/nhm.2025045-11 doi: 10.1016/S0096-3003(01)00291-0 – ident: key-10.3934/nhm.2025045-52 doi: 10.1016/j.apnum.2022.09.012 – ident: key-10.3934/nhm.2025045-3 doi: 10.1109/TSMC.2022.3152505 – ident: key-10.3934/nhm.2025045-47 – ident: key-10.3934/nhm.2025045-19 doi: 10.4208/ijnam2025-1020 – ident: key-10.3934/nhm.2025045-43 doi: 10.1080/00036811.2024.2302405 – ident: key-10.3934/nhm.2025045-23 doi: 10.1111/sapm.12763 – ident: key-10.3934/nhm.2025045-57 doi: 10.2478/cmam-2009-0010 – ident: key-10.3934/nhm.2025045-17 doi: 10.1016/j.bulsci.2025.103637 – ident: key-10.3934/nhm.2025045-49 doi: 10.1007/s00365-021-09549-y – ident: key-10.3934/nhm.2025045-45 doi: 10.1007/s10483-024-3149-8 – ident: key-10.3934/nhm.2025045-44 doi: 10.1016/j.cma.2020.113547 – ident: key-10.3934/nhm.2025045-54 doi: 10.1007/s10444-007-9058-z – ident: key-10.3934/nhm.2025045-15 – ident: key-10.3934/nhm.2025045-67 doi: 10.3934/nhm.2024048 – ident: key-10.3934/nhm.2025045-9 doi: 10.1016/j.apnum.2019.08.028 – ident: key-10.3934/nhm.2025045-34 doi: 10.1145/3689037 – ident: key-10.3934/nhm.2025045-62 doi: 10.1016/j.aml.2012.02.018 – ident: key-10.3934/nhm.2025045-33 doi: 10.1051/proc/202373048 |
| SSID | ssj0043703 |
| Score | 2.341254 |
| Snippet | In this work, we design an iteration-based unsupervised neural network algorithm and the theoretical bound of the loss function through Barron space to solve... |
| SourceID | doaj crossref |
| SourceType | Open Website Index Database |
| StartPage | 1026 |
| SubjectTerms | barron space boundary layer in singular perturbation convergence analysis mi-pinn multiple scale problems multiple scale problems in 1d and 2d neural network pinn strongly coupled system unsteady mhd flow |
| Title | A modified iterative PINN algorithm for strongly coupled system of boundary layer originated convection diffusion reaction problems in MHD flows with analysis |
| URI | https://doaj.org/article/ee2acb9ef8324f039189d6bd3b7d3196 |
| Volume | 20 |
| WOSCitedRecordID | wos001587183400004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals issn: 1556-1801 databaseCode: DOA dateStart: 20230101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.doaj.org/ omitProxy: false ssIdentifier: ssj0043703 providerName: Directory of Open Access Journals |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07bxsxDBaKoEOX9I0mfYBD10N8j-ik0X0EGVqjQwt4O-goyjZwuQt8dgr_mf7Wkie1cKcsXQVBEMRP1EdC_KjUeyxnLfo2z4zDNqu0NpmzwWSe0UUFVsyCp0LhL_ViYZZL--2o1Zf8CYvywPHgLogKXsVSYOhVQfTMjfW69WVbe4GPeN9Zbf8EU9EHV2U99UTmx1JnOTvhWJlX2rK66NdSgC7KXZf_vEVHkv3T23L1RJ0mUgjzuJmn6gH1z9TjRBAhXb_xufo1h5vBb4KMRjlk9lXAgfkCXLcaOM5f3wCzUBglwb3qDoDD_rbj2VGwGYYA7dRHaXuAzjHbhtQYi3knTB_QpzIHkLYpe8mjAXPKOJQ6z4yw6eHr9ScI3fBzBEnjgkvCJi_Uj6vP3z9eZ6nBQoaF1buMLBrhe8QkymkqAuXER-dczUFb8Kgt8v30vnTWOo9Ocoa-Jm2oII3alS_VST_09EqBxdZhjnWZt1SZS22wmNmZZ_aAwZAJZwyLdNTNbdTRaDj-EIs0bJEmWeRMfRAz_J0i4tfTAEOiSZBo7oPE-f9Y5LV6JHuK2ZY36mS33dNb9RDvdptx-25C22-jNd60 |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+modified+iterative+PINN+algorithm+for+strongly+coupled+system+of+boundary+layer+originated+convection+diffusion+reaction+problems+in+MHD+flows+with+analysis&rft.jtitle=Networks+and+heterogeneous+media&rft.au=Arihant+Patawari&rft.au=Shridhar+Kumar&rft.au=Pratibhamoy+Das&rft.date=2025-01-01&rft.pub=AIMS+Press&rft.issn=1556-1801&rft.volume=20&rft.issue=3&rft.spage=1026&rft.epage=1060&rft_id=info:doi/10.3934%2Fnhm.2025045&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_ee2acb9ef8324f039189d6bd3b7d3196 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1556-1801&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1556-1801&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1556-1801&client=summon |