<p>This study presents the development and performance evaluation of a deep-learned finite element (DLFE) model for solving 2D heat conduction problems. The DLFE employs a deep neural network to predict the temperature–gradient interpolation matrix on the basis of data generated from high-density meshes, improving the accuracy of thermal conductivity representation. In this study, the prediction error was reduced by more than half by switching the learning coordinate system for the gradient calculation from the global coordinate system to the natural coordinate system. Additionally, the postprocessing of network outputs was simplified using the Jacobian matrix, which is in line with traditional methods. The proposed DLFE was evaluated via a series of numerical experiments, including comparisons with conventional 8-node (Q8) and 9-node (Q9) finite elements. Although DLFE exhibited similar accuracy to conventional elements in standard heat conduction cases, it outperformed them in cases with localized heat flux concentrations, where typically higher mesh refinement is required. In such cases, DLFE provides more accurate results with fewer mesh elements, whereas conventional methods typically require greater mesh refinement. Consequently, DLFE has proven to be a computationally efficient alternative for accurate thermal analysis in high heat flux environments. This approach suggests that DLFE provides effective solutions for the thermal design and analysis of systems subjected to extreme localized thermal loads.</p>

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Development and performance analysis of a deep-learned finite element for 2D heat conduction on the natural coordinate system

  • Younghwan Joo,
  • Jaeho Jung

摘要

This study presents the development and performance evaluation of a deep-learned finite element (DLFE) model for solving 2D heat conduction problems. The DLFE employs a deep neural network to predict the temperature–gradient interpolation matrix on the basis of data generated from high-density meshes, improving the accuracy of thermal conductivity representation. In this study, the prediction error was reduced by more than half by switching the learning coordinate system for the gradient calculation from the global coordinate system to the natural coordinate system. Additionally, the postprocessing of network outputs was simplified using the Jacobian matrix, which is in line with traditional methods. The proposed DLFE was evaluated via a series of numerical experiments, including comparisons with conventional 8-node (Q8) and 9-node (Q9) finite elements. Although DLFE exhibited similar accuracy to conventional elements in standard heat conduction cases, it outperformed them in cases with localized heat flux concentrations, where typically higher mesh refinement is required. In such cases, DLFE provides more accurate results with fewer mesh elements, whereas conventional methods typically require greater mesh refinement. Consequently, DLFE has proven to be a computationally efficient alternative for accurate thermal analysis in high heat flux environments. This approach suggests that DLFE provides effective solutions for the thermal design and analysis of systems subjected to extreme localized thermal loads.