Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks
This study investigates a simulation-based approach to the inverse problem of two-dimensional steady-state heat conduction in flat plates by employing Physics-Informed Neural Networks (PINNs). The primary objective is to reconstruct the temperature field and deduce unknown boundary conditions using...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Eng |
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| Online Access: | https://www.mdpi.com/2673-4117/6/5/99 |
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| author | Yufan Pan Ke Zhang Ji Zhang Ning Mei |
| author_facet | Yufan Pan Ke Zhang Ji Zhang Ning Mei |
| author_sort | Yufan Pan |
| collection | DOAJ |
| description | This study investigates a simulation-based approach to the inverse problem of two-dimensional steady-state heat conduction in flat plates by employing Physics-Informed Neural Networks (PINNs). The primary objective is to reconstruct the temperature field and deduce unknown boundary conditions using limited labeled data sourced from conventional numerical methods. This work specifically validates the methodology using simulated data with known original conditions, rather than addressing truly unknown boundary conditions in real-world scenarios. By leveraging PINNs, the approach integrates physical laws with data-driven learning, facilitating the efficient inversion of boundary conditions and precise reconstruction of the temperature field. Within a temperature range of 10 °C to 40 °C, the method consistently achieves an average relative error of less than 10% and maintains an absolute error within 1 °C across the computational domain. By optimizing the distribution of sample points without increasing their quantity, the average relative error is further reduced by approximately 1%, thereby enhancing inversion accuracy. Additionally, implementing an adaptive weight adjustment strategy, based on learning rate annealing, further refines the method, reducing the maximum absolute error by 0.4 °C and the average relative error by 2% when compared to traditional PINNs. This research demonstrates the capability of PINNs to provide a rapid and effective solution for inverse heat conduction problems, establishing a foundation for their potential application in addressing complex inverse heat transfer challenges. |
| format | Article |
| id | doaj-art-dc7d7994cd884c69b431850dd0a583c7 |
| institution | DOAJ |
| issn | 2673-4117 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Eng |
| spelling | doaj-art-dc7d7994cd884c69b431850dd0a583c72025-08-20T03:14:34ZengMDPI AGEng2673-41172025-05-01659910.3390/eng6050099Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural NetworksYufan Pan0Ke Zhang1Ji Zhang2Ning Mei3College of Engineering, Ocean University of China, 239 Songling Road, Qingdao 266100, ChinaCollege of Engineering, Ocean University of China, 239 Songling Road, Qingdao 266100, ChinaCollege of Engineering, Ocean University of China, 239 Songling Road, Qingdao 266100, ChinaCollege of Engineering, Ocean University of China, 239 Songling Road, Qingdao 266100, ChinaThis study investigates a simulation-based approach to the inverse problem of two-dimensional steady-state heat conduction in flat plates by employing Physics-Informed Neural Networks (PINNs). The primary objective is to reconstruct the temperature field and deduce unknown boundary conditions using limited labeled data sourced from conventional numerical methods. This work specifically validates the methodology using simulated data with known original conditions, rather than addressing truly unknown boundary conditions in real-world scenarios. By leveraging PINNs, the approach integrates physical laws with data-driven learning, facilitating the efficient inversion of boundary conditions and precise reconstruction of the temperature field. Within a temperature range of 10 °C to 40 °C, the method consistently achieves an average relative error of less than 10% and maintains an absolute error within 1 °C across the computational domain. By optimizing the distribution of sample points without increasing their quantity, the average relative error is further reduced by approximately 1%, thereby enhancing inversion accuracy. Additionally, implementing an adaptive weight adjustment strategy, based on learning rate annealing, further refines the method, reducing the maximum absolute error by 0.4 °C and the average relative error by 2% when compared to traditional PINNs. This research demonstrates the capability of PINNs to provide a rapid and effective solution for inverse heat conduction problems, establishing a foundation for their potential application in addressing complex inverse heat transfer challenges.https://www.mdpi.com/2673-4117/6/5/99physics-informed neural networksheat transfer inverse problemdeep learningboundary conditionstwo-dimensional steady-state thermal conductivity |
| spellingShingle | Yufan Pan Ke Zhang Ji Zhang Ning Mei Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks Eng physics-informed neural networks heat transfer inverse problem deep learning boundary conditions two-dimensional steady-state thermal conductivity |
| title | Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks |
| title_full | Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks |
| title_fullStr | Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks |
| title_full_unstemmed | Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks |
| title_short | Research on the Reconstruction of the Temperature Field in Two-Dimensional Steady-State Thermal Conductivity Based on Physics-Informed Neural Networks |
| title_sort | research on the reconstruction of the temperature field in two dimensional steady state thermal conductivity based on physics informed neural networks |
| topic | physics-informed neural networks heat transfer inverse problem deep learning boundary conditions two-dimensional steady-state thermal conductivity |
| url | https://www.mdpi.com/2673-4117/6/5/99 |
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