A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model
IntroductionBiot's consolidation model in poroelasticity describes the interaction between the fluid and the deformable porous structure. Based on the fixed-stress splitting iterative method proposed by Mikelic et al. (Computat Geosci, 2013), we present a network approach to solve Biot's c...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-08-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2023.1206500/full |
| _version_ | 1797755366055870464 |
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| author | Mingchao Cai Huipeng Gu Pengxiang Hong Jingzhi Li |
| author_facet | Mingchao Cai Huipeng Gu Pengxiang Hong Jingzhi Li |
| author_sort | Mingchao Cai |
| collection | DOAJ |
| description | IntroductionBiot's consolidation model in poroelasticity describes the interaction between the fluid and the deformable porous structure. Based on the fixed-stress splitting iterative method proposed by Mikelic et al. (Computat Geosci, 2013), we present a network approach to solve Biot's consolidation model using physics-informed neural networks (PINNs).MethodsTwo independent and small neural networks are used to solve the displacement and pressure variables separately. Accordingly, separate loss functions are proposed, and the fixed stress splitting iterative algorithm is used to couple these variables. Error analysis is provided to support the capability of the proposed fixed-stress splitting-based PINNs (FS-PINNs).ResultsSeveral numerical experiments are performed to evaluate the effectiveness and accuracy of our approach, including the pure Dirichlet problem, the mixed partial Neumann and partial Dirichlet problem, and the Barry-Mercer's problem. The performance of FS-PINNs is superior to traditional PINNs, demonstrating the effectiveness of our approach.DiscussionOur study highlights the successful application of PINNs with the fixed-stress splitting iterative method to tackle Biot's model. The ability to use independent neural networks for displacement and pressure offers computational advantages while maintaining accuracy. The proposed approach shows promising potential for solving other similar geoscientific problems. |
| first_indexed | 2024-03-12T17:46:49Z |
| format | Article |
| id | doaj.art-a1344b0f8f974b8eb321ec2e8910e38d |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-03-12T17:46:49Z |
| publishDate | 2023-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-a1344b0f8f974b8eb321ec2e8910e38d2023-08-03T16:24:25ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872023-08-01910.3389/fams.2023.12065001206500A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's modelMingchao Cai0Huipeng Gu1Pengxiang Hong2Jingzhi Li3Department of Mathematics, Morgan State University, Baltimore, MD, United StatesDepartment of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, ChinaDepartment of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, ChinaDepartment of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, ChinaIntroductionBiot's consolidation model in poroelasticity describes the interaction between the fluid and the deformable porous structure. Based on the fixed-stress splitting iterative method proposed by Mikelic et al. (Computat Geosci, 2013), we present a network approach to solve Biot's consolidation model using physics-informed neural networks (PINNs).MethodsTwo independent and small neural networks are used to solve the displacement and pressure variables separately. Accordingly, separate loss functions are proposed, and the fixed stress splitting iterative algorithm is used to couple these variables. Error analysis is provided to support the capability of the proposed fixed-stress splitting-based PINNs (FS-PINNs).ResultsSeveral numerical experiments are performed to evaluate the effectiveness and accuracy of our approach, including the pure Dirichlet problem, the mixed partial Neumann and partial Dirichlet problem, and the Barry-Mercer's problem. The performance of FS-PINNs is superior to traditional PINNs, demonstrating the effectiveness of our approach.DiscussionOur study highlights the successful application of PINNs with the fixed-stress splitting iterative method to tackle Biot's model. The ability to use independent neural networks for displacement and pressure offers computational advantages while maintaining accuracy. The proposed approach shows promising potential for solving other similar geoscientific problems.https://www.frontiersin.org/articles/10.3389/fams.2023.1206500/fullphysics-informed neural networksthe fixed-stress methodBiot's modeliterative algorithmseparated networks |
| spellingShingle | Mingchao Cai Huipeng Gu Pengxiang Hong Jingzhi Li A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model Frontiers in Applied Mathematics and Statistics physics-informed neural networks the fixed-stress method Biot's model iterative algorithm separated networks |
| title | A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model |
| title_full | A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model |
| title_fullStr | A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model |
| title_full_unstemmed | A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model |
| title_short | A combination of physics-informed neural networks with the fixed-stress splitting iteration for solving Biot's model |
| title_sort | combination of physics informed neural networks with the fixed stress splitting iteration for solving biot s model |
| topic | physics-informed neural networks the fixed-stress method Biot's model iterative algorithm separated networks |
| url | https://www.frontiersin.org/articles/10.3389/fams.2023.1206500/full |
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