NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations
The exploration of deep learning methodologies has recently generated significant interest in the use of Physics-Informed Neural Networks (PINNs) to address complex physical problems governed by partial differential equations (PDEs). The PINN is trained using information from physical laws, includin...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Engineering Applications of Computational Fluid Mechanics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/19942060.2025.2535015 |
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| author | Xin Qi Dawei Zhang Fan Wang Wuxia Bi Mingda Lu |
| author_facet | Xin Qi Dawei Zhang Fan Wang Wuxia Bi Mingda Lu |
| author_sort | Xin Qi |
| collection | DOAJ |
| description | The exploration of deep learning methodologies has recently generated significant interest in the use of Physics-Informed Neural Networks (PINNs) to address complex physical problems governed by partial differential equations (PDEs). The PINN is trained using information from physical laws, including governing PDEs, boundary conditions, and initial conditions. However, achieving a well-trained PINN typically necessitates an appropriate balance between the weights of each loss function, which can considerably increase manual effort. This paper introduces a novel training approach that integrates non-dimensionalization with a multi-task learning technique, termed Automatic Weighted Loss (AWL), to autonomously achieve an optimal balance for each loss function. In the baseline PINN training for solving time-dependent PDEs, multiple weights (usually more than six) must be manually tuned for the model, whereas this method can reduce the number of scaling weights to only one. The proposed approach, referred to as the Non-dimensionalization Automatic Weighted Loss (NDAWL), is evaluated through six free-surface flow problems modelled by the Shallow Water Equations (SWEs). Furthermore, a comparative analysis is conducted between the solutions obtained using NDAWL-PINN and those from the original PINN, which relies on manual fine-tuning of loss functions. The numerical results indicate that the NDAWL-PINN method achieves comparable or superior accuracy to the original PINN, demonstrating its effectiveness in automating the balancing of loss functions. |
| format | Article |
| id | doaj-art-4e9029e76c0c427883243873efd5026f |
| institution | DOAJ |
| issn | 1994-2060 1997-003X |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Engineering Applications of Computational Fluid Mechanics |
| spelling | doaj-art-4e9029e76c0c427883243873efd5026f2025-08-20T02:41:29ZengTaylor & Francis GroupEngineering Applications of Computational Fluid Mechanics1994-20601997-003X2025-12-0119110.1080/19942060.2025.2535015NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equationsXin Qi0Dawei Zhang1Fan Wang2Wuxia Bi3Mingda Lu4State Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, People’s Republic of ChinaState Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, People’s Republic of ChinaState Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, People’s Republic of ChinaState Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, People’s Republic of ChinaState Key Laboratory of Water Cycle and Water Security, China Institute of Water Resources and Hydropower Research, Beijing, People’s Republic of ChinaThe exploration of deep learning methodologies has recently generated significant interest in the use of Physics-Informed Neural Networks (PINNs) to address complex physical problems governed by partial differential equations (PDEs). The PINN is trained using information from physical laws, including governing PDEs, boundary conditions, and initial conditions. However, achieving a well-trained PINN typically necessitates an appropriate balance between the weights of each loss function, which can considerably increase manual effort. This paper introduces a novel training approach that integrates non-dimensionalization with a multi-task learning technique, termed Automatic Weighted Loss (AWL), to autonomously achieve an optimal balance for each loss function. In the baseline PINN training for solving time-dependent PDEs, multiple weights (usually more than six) must be manually tuned for the model, whereas this method can reduce the number of scaling weights to only one. The proposed approach, referred to as the Non-dimensionalization Automatic Weighted Loss (NDAWL), is evaluated through six free-surface flow problems modelled by the Shallow Water Equations (SWEs). Furthermore, a comparative analysis is conducted between the solutions obtained using NDAWL-PINN and those from the original PINN, which relies on manual fine-tuning of loss functions. The numerical results indicate that the NDAWL-PINN method achieves comparable or superior accuracy to the original PINN, demonstrating its effectiveness in automating the balancing of loss functions.https://www.tandfonline.com/doi/10.1080/19942060.2025.2535015Physics-informed neural networkNone-dimensionalizationmulti-task learningshallow water equationsfree-surface flow |
| spellingShingle | Xin Qi Dawei Zhang Fan Wang Wuxia Bi Mingda Lu NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations Engineering Applications of Computational Fluid Mechanics Physics-informed neural network None-dimensionalization multi-task learning shallow water equations free-surface flow |
| title | NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations |
| title_full | NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations |
| title_fullStr | NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations |
| title_full_unstemmed | NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations |
| title_short | NDAWL-PINN: a new non-dimensionalization and multi-task learning approach for efficient training of physics-informed neural networks to solve the shallow water equations |
| title_sort | ndawl pinn a new non dimensionalization and multi task learning approach for efficient training of physics informed neural networks to solve the shallow water equations |
| topic | Physics-informed neural network None-dimensionalization multi-task learning shallow water equations free-surface flow |
| url | https://www.tandfonline.com/doi/10.1080/19942060.2025.2535015 |
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