A framework based on experimental-and-auxiliary data fusion and robust multi-task neural networks for the prediction of melting points in electroslag systems

Abstract

The melting point of slag plays a pivotal role in determining the process stability and product quality during electroslag remelting (ESR). However, accurate prediction remains challenging due to the scarcity of experimental data, the compositional complexity of slag systems, and the limited accuracy of conventional empirical models. In this study, a robust multi-task neural network framework based on experimental-and-auxiliary data fusion is developed to predict the melting points of ESR slags. The framework combines one experimental melting-point source dataset with two auxiliary augmented datasets: (i) experimentally measured melting points, (ii) melting-point estimates derived from viscosity inflection points using the viscosity prediction model, and (iii) melting-point values generated from empirical correlations. A multi-task learning architecture is constructed, comprising one primary task (experimental data) and two auxiliary tasks (augmented datasets), enabling effective knowledge transfer and joint optimization through a custom-designed loss function and adaptive task-weighting scheme. Error analysis results demonstrate that the proposed method consistently outperforms traditional machine learning models and single-task neural networks across multiple evaluation metrics, including mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). In addition, the model exhibits excellent robustness and physical consistency, providing a promising solution for intelligent slag system design and process optimization in ESR operations.

Keywords

machine learning / melting point / slag / multi-task learning / data fusion / inflection points

References

[1] Shi CB. Deoxidation of electroslag remelting (ESR)–A review. ISIJ Int., 2020, 60(6):1083.

[2] Shi CB, Huang Y, Zhang JX, Li J, Zheng X. Review on desulfurization in electroslag remelting. Int. J. Miner. Metall. Mater., 2021, 28(1):18.

[3] Shi CB, Wang SJ, Li J, Cho JW. Non-metallic inclusions in electroslag remelting: A review. J. Iron Steel Res. Int., 2021, 28(12):1483.

[4] Hou D, Wang DY, Zhou XZ, Hu SY, Wang HH, Qu TP. Study on physical and chemical properties of slag used for electroslag remelting of superalloy containing titanium and aluminum. Metall. Mater. Trans. B, 2022, 53(5):2972.

[5] X.F. Shi, Y. Wang, B.J. Wang, and L.Z. Chang, Effect of basicity and Al₂O₃ content in slag on cleanliness of electroslag ingot, Metals, 13(2023), No. 4, art. No. 642.

[6] Zheng DL, Li J, Shi CB. Development of low-fluoride slag for electroslag remelting: Role of Li₂O on the crystallization and evaporation of the slag. ISIJ Int., 2020, 60(5):840.

[7] D. Hou, P. Pan, D.Y. Wang, S.Y. Hu, H.H. Wang, and G.G. Zhang, Study on the melting temperature of CaF_2–CaO–MgO–Al₂O_3–TiO₂ slag under the condition of a fixed ratio of titanium and aluminum in the steel during the electroslag remelting process, Materials, 14(2021), No. 20, art. No. 6047.

[8] Wang WL, Yan X, Zhou LJ, Xie SL, Huang DY. Influences of basicity and Li₂O on the properties of fluorine-free mold flux for the casting of medium carbon steels. Metall. Mater. Trans. B, 2016, 47(2):963.

[9] Huang Y, Shi CB, Wan XX, Li JL, Zheng DL, Li J. Effect of SiO₂ and B₂O₃ on crystallization and structure of CaF_2–CaO–Al₂O₃-based slag for electroslag remelting of ultra-supercritical rotor steel. J. Iron Steel Res. Int., 2021, 28(12):1530.

[10] Du YX, Dong YW, Jiang ZH, et al.Dissolution kinetics and reaction mechanism of Al₂O₃ in molten CaF_2–CaO–Al₂O₃ slag. J. Iron Steel Res. Int., 2024, 31(4):861.

[11] Qiu JY, Wang H, Huo GJ, Liu CJ. Phase diagram of CaO–Al₂O_3–CeO_x slag system at 1600°C in reducing atmosphere and air atmosphere. Ceram. Int., 2023, 49(12):20447.

[12] J.Y. Qiu, W.J. Li, C.J. Liu, and M.F. Jiang, Phase equilibria of CaO–Al₂O_3–Ti₂O₃ system at 1500°C and 1600°C in C/CO equilibrium atmosphere, J. Non-Cryst. Solids, 648(2025), art. No. 123312.

[13] Qiu JY, Liu CJ, Yu Z. Isothermal section of CaO–SiO_2–La₂O₃ system within specific region at 1673–1473 K. Ceram. Int., 2018, 44(11):12564.

[14] Itaya H, Watanabe T, Hayashi M, Nagata K. Phase diagram of FeO–TiO_2–SiO_2–5%Al₂O₃ slag (phase diagram of smelting slag of titanium oxide bearing iron sand). ISIJ Int., 2014, 54(5):1067.

[15] Liu Y, Wang Y, Li GQ, Yuan C, Lu R, Li BK. Investigation on the structure, fluoride vaporization and crystallization behavior of CaF_2–CaO–Al₂O_3–(SiO₂) slag for electroslag remelting. J. Therm. Anal. Calorim., 2020, 139(2):923.

[16] X.J. Wang, H.B. Jin, L.G. Zhu, et al., Effect of CaF₂ on the viscosity and microstructure of CaO–SiO_2–Al₂O₃ based continuous casting mold flux, Metals, 9(2019), No. 8, art. No. 871.

[17] Ma J, Li W, Fu GQ, Zhu MY. Effect of Al₂O₃ on the viscosity and crystallization behavior of CaO–SiO_2–MgO–Al₂O_3–TiO_2–Cr₂O₃ slag. JOM, 2022, 74(1):159.

[18] Chen X, Dong YW, Jiang ZH, Wang J, Liu YX. Prediction of titanium burn-off and untimate titanium content in electroslag process. J. Mater. Res. Technol., 2024, 32: 1648.

[19] Liu YX, Dong YW, Jiang ZH, Chen X. Interpretable predictive model for inclusions in electroslag remelting based on XGBoost and SHAP analysis. Metall. Mater. Trans. B, 2024, 55(3):1428.

[20] DebRoy T, Mukherjee T, Wei HL, Elmer JW, Milewski JO. Metallurgy, mechanistic models and machine learning in metal printing. Nat. Rev. Mater., 2021, 6(1):48.

[21] Li YR, Fu ZH, Yu XY, et al.Developing an atmospheric aging evaluation model of acrylic coatings: A semi-supervised machine learning algorithm. Int. J. Miner. Metall. Mater., 2024, 31(7):1617.

[22] Kuang JG, Long ZL. Prediction model for corrosion rate of low-alloy steels under atmospheric conditions using machine learning algorithms. Int. J. Miner. Metall. Mater., 2024, 31(2):337.

[23] R. Datta, R. Ramprasad, and S. Venkatram, Conductivity prediction model for ionic liquids using machine learning, J. Chem. Phys., 156(2022), No. 21, art. No. 214505.

[24] Chen X, Dong YW, Jiang ZH, Liu YX, Na XW. Enhancement of the electrical conductivity calculation model for CaO-based slag systems through machine learning assistance. JOM, 2025, 77(5):3661.

[25] Chen ZW, Wang MH, Meng Z, Wang H, Liu LL, Wang XD. Development of structure-informed artificial neural network for accurately modeling viscosity of multicomponent molten slags. Ceram. Int., 2021, 47(21):30691.

[26] Xie H, Ling JW, Guo J, et al.Sulfide capacity model for multicomponent molten slag based on artificial neural network. Metall. Mater. Trans. B, 2023, 54(6):3324.

[27] W. Yan, Y.Y. Shen, S.J. Chen, and Y.Y. Wang, Viscosity and melting temperature prediction of mold fluxes based on explainable machine learning and SHapley additive explanations, J. Non-Cryst. Solids, 636(2024), art. No. 123037.

[28] K. Low, R. Kobayashi, and E.I. Izgorodina, The effect of descriptor choice in machine learning models for ionic liquid melting point prediction, J. Chem. Phys., 153(2020), No. 10, art. No. 104101.

[29] H. Meng, Y.W. Liu, H.L. Yu, L. Zhuang, and Y.H. Chu, Machine-learning-potential-driven prediction of high-entropy ceramics with ultra-high melting points, Cell Rep. Phys. Sci., 6(2025), No. 2, art. No. 102449.

[30] J.L. Gao, Y. Tong, H. Zhang, et al., Machine learning assisted design of Ni-based superalloys with excellent high-temperature performance, Mater. Charact., 198(2023), art. No. 112740.

[31] Kankanamge UMHU, Reiner J, Ma XJ, Gallo SC, Xu W. Machine learning guided alloy design of high-temperature NiTiHf shape memory alloys. J. Mater. Sci., 2022, 57(41):19447.

[32] Y. Zhou, P. Srinivasan, F. Körmann, et al., Thermodynamics up to the melting point in a TaVCrW high entropy alloy: Systematic ab initio study aided by machine learning potentials, Phys. Rev. B, 105(2022), No. 21, art. No. 214302.

[33] H.M. Chen, Z.W. Shang, W.C. Lu, M.J. Li, and F.P. Tan, A property-driven stepwise design strategy for multiple low-melting alloys via machine learning, Adv. Eng. Mater., 23(2021), No. 12, art. No. 2100612.

[34] Y.M. Wu, Z.W. Shang, T. Lu, W.Y. Zhou, M.J. Li, and W.C. Lu, Target- directed discovery for low melting point alloys via inverse design strategy, J. Alloy. Compd., 971(2024), art. No. 172664.

[35] F.Z. Dai, Y.F. Xu, J.D. Hu, S.P. Zhu, and X.F. Gu, Boosting the melting point record to 4431 K: Simulated with machine learning potential at SCAN accuracy, J. Am. Ceram. Soc., 108(2025), No. 5, art. No. e20356.

[36] Shahbazian F, Du SC, Seetharaman S. Viscosities of some fayalitic slags containing CaF₂. ISIJ Int., 1999, 39(7):687.

[37] Chen X, Dong YW, Jiang ZH, Liu YX. Predicting the viscosity of CaF2-based slag and reverse design of electroslag systems using explainable machine learning. Metall. Mater. Trans. B, 2025, 56(3):3125.

[38] He SP, Wang S, Jia BR, Li M, Wang QQ, Wang Q. Molecular dynamics simulation of the structure and properties of CaO–SiO_2–CaF₂ slag systems. Metall. Mater. Trans. B, 2019, 50(3):1503.

[39] Zhao XH, Zhang ZH, Ju JT, Jiao ZY, Liu JP. Study on melting temperature of CaF_2–SiO_2–Al₂O_3–CaO–MgO slag. Hot Working Technol., 2013, 42(9):81.

Rights & permissions

University of Science and Technology Beijing