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The DeepXDE
framework for solving transient heat conduction problems
Xiaoyang Feng, Zhijuan Meng, Heng Cheng and Lidong Ma |
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Vol. 20 (2025), No. 3, 363–376
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DOI: 10.2140/jomms.2025.20.363
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Abstract |
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This paper proposes a phased optimization physical information neural networks (PINNs) method based on the DeepXDE framework, which is used to solve transient heat conduction equations. By combining the Adam and L-BFGS hybrid optimization strategy, this method achieves rapid convergence and demonstrates superior performance in one-dimensional to three-dimensional heat conduction problems. Through comparative experiments, the influence laws of neural network structure parameters (such as the number of hidden layers and the number of neurons) on the solution accuracy are clarified, and the optimal network structure configuration is established. The tanh activation function with second-order derivatives is adopted to avoid the problem of gradient disappearance effectively, and the governing equations and boundary conditions are seamlessly integrated into the loss function, achieving a true meshless solution. The numerical experimental results show that this method can accurately capture the spatiotemporal evolution characteristics of the temperature field. |
Keywords
deep learning, neural network, DeepXDE, heat conduction
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Milestones
Received: 28 April 2025
Revised: 17 June 2025
Accepted: 15 July 2025
Published: 2 September 2025
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Authors |
| Xiaoyang Feng | |
| School of Applied Science Taiyuan University of Science and Technology Taiyuan, 030024 China |
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| Zhijuan Meng | |
| School of Applied Science Taiyuan University of Science and Technology Taiyuan, 030024 China |
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| Heng Cheng | |
| School of Applied Science Taiyuan University of Science and Technology Taiyuan, 030024 China |
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| Lidong Ma | |
| School of Applied Science Taiyuan University of Science and Technology Taiyuan, 030024 China |
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| © 2025 MSP (Mathematical Sciences Publishers). |
