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<p>The temperature field distribution during the electroslag remelting (ESR) process directly governs the solidification behavior and microstructural characteristics of the ingot. However, direct observation of the internal temperature field is severely constrained by the high-temperature sealed environment, while conventional finite element methods encounter substantial challenges including high parameter sensitivity, prohibitive computational costs, and inefficient data utilization, rendering them inadequate for real-time reconstruction requirements. This study innovatively applies physics-informed neural networks to ESR temperature field reconstruction by constructing a deep neural network architecture comprising 7 hidden layers with 131,201 trainable parameters. The two-dimensional axisymmetric steady-state heat conduction equation, four categories of boundary conditions, and physical constraints are embedded into a multi-objective loss function through automatic differentiation techniques. To address the sparsity challenge of merely 60 measurement points extracted from peer-reviewed literature,a three-stage adaptive weight scheduling strategy and differentiated data weighting mechanism are proposed, wherein weight factors of 120 are imposed on critical regions near the liquidus and solidus isotherms. After 12,000 training iterations, the model achieves remarkable overall prediction accuracy with RMSE of 56.38&#xa0;K and <i>R</i><sup>2</sup> of 0.9333, while attaining exceptional precision at the liquidus (1763&#xa0;K) and solidus (1473&#xa0;K) with prediction errors of only 3.56&#xa0;K and 5.75&#xa0;K, respectively, corresponding to spatial localization errors of merely 2 to 3&#xa0;mm. The reconstructed temperature field accurately reproduces the characteristic “U-shaped” molten pool morphology, with PDE residual relative errors of only 1.5&#xa0;pct, demonstrating robust physical consistency. Comparative analysis with traditional machine learning approaches reveals significant superiority of PINNs in both prediction accuracy and physical fidelity. This research provides an efficient tool for real-time monitoring and process optimization of ESR operations, holding substantial significance for advancing the metallurgical field toward a data-physics integrated paradigm.</p>

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Rapid Temperature Field Reconstruction for Electroslag Remelting Using Physics-Informed Neural Networks

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Ao Wang,
  • Xi Chen,
  • Yiming Li,
  • Zhouhua Jiang,
  • Zonghao Zhang

摘要

The temperature field distribution during the electroslag remelting (ESR) process directly governs the solidification behavior and microstructural characteristics of the ingot. However, direct observation of the internal temperature field is severely constrained by the high-temperature sealed environment, while conventional finite element methods encounter substantial challenges including high parameter sensitivity, prohibitive computational costs, and inefficient data utilization, rendering them inadequate for real-time reconstruction requirements. This study innovatively applies physics-informed neural networks to ESR temperature field reconstruction by constructing a deep neural network architecture comprising 7 hidden layers with 131,201 trainable parameters. The two-dimensional axisymmetric steady-state heat conduction equation, four categories of boundary conditions, and physical constraints are embedded into a multi-objective loss function through automatic differentiation techniques. To address the sparsity challenge of merely 60 measurement points extracted from peer-reviewed literature,a three-stage adaptive weight scheduling strategy and differentiated data weighting mechanism are proposed, wherein weight factors of 120 are imposed on critical regions near the liquidus and solidus isotherms. After 12,000 training iterations, the model achieves remarkable overall prediction accuracy with RMSE of 56.38 K and R2 of 0.9333, while attaining exceptional precision at the liquidus (1763 K) and solidus (1473 K) with prediction errors of only 3.56 K and 5.75 K, respectively, corresponding to spatial localization errors of merely 2 to 3 mm. The reconstructed temperature field accurately reproduces the characteristic “U-shaped” molten pool morphology, with PDE residual relative errors of only 1.5 pct, demonstrating robust physical consistency. Comparative analysis with traditional machine learning approaches reveals significant superiority of PINNs in both prediction accuracy and physical fidelity. This research provides an efficient tool for real-time monitoring and process optimization of ESR operations, holding substantial significance for advancing the metallurgical field toward a data-physics integrated paradigm.