Multiobjective optimization of dielectric, thermal, and mechanical properties of inorganic glasses utilizing explainable machine learning and genetic algorithm

Abstract

To meet the demands of advanced electronic devices, inorganic glasses are required to have comprehensive dielectric, thermal, and mechanical properties. However, the complex composition–property relationship and vast compositional diversity hinder optimization. This study developed machine learning models to predict permittivity, dielectric loss, thermal conductivity, coefficient of thermal expansion, and Young’s modulus based on the composition features of inorganic glasses. The optimal models achieve R² values of 0.9614, 0.7411, 0.9454, 0.9684, and 0.8164, respectively. By integrating domain knowledge with model-agnostic interpretation methods, feature contributions and interactions were analyzed. The mixed alkali effect is crucial for property regulation, especially Na-K for dielectric loss and Na-Li for thermal conductivity. Boron anomaly shifts the high-λ region to a balanced composition of alkali metals with rising B%. The multiobjective optimization of properties was realized using a genetic algorithm framework. After 23 iterations, the optimal material in the MgO-Al₂O₃-B₂O₃-SiO₂ system exhibits ε_r = 4.78, tanδ = 0.00063, λ = 2.59 W/(m·K), α = 50.27×10⁻⁷K⁻¹, and E = 82.41 GPa, outperforming all materials in the dataset. The computational effort was reduced to 1/19 of that required using exhaustive search methods. This study provides a model interpretation framework and an effective multiobjective optimization strategy for glass design.

Keywords

genetic algorithm / inorganic glass / machine learning / model-agnostic interpretation / multiobjective optimization

References

[1] Rappaport TS, Xing Y, Kanhere O, et al. Wireless communications and applications above 100 GHz: Opportunities and challenges for 6G and beyond. IEEE Access. 2019; 7: 78729-78757.

[2] Dang S, Amin O, Shihada B, Alouini M.-S. What should 6G be? Nature Electronics. 2020; 3(1): 20-29.

[3] Hong S, Lee CS, Lee MH, et al. Ultralow-dielectric-constant amorphous boron nitride. Nature. 2020; 582(7813): 511-514.

[4] Hill MD, Cruickshank DB, MacFarlane IA. Perspective on ceramic materials for 5G wireless communication systems. Appl Phys Lett. 2021; 118(12).

[5] Yang H, Zhang S, Yang H, et al. The latest process and challenges of microwave dielectric ceramics based on pseudo phase diagrams. J Adv Ceram. 2021; 10(5): 885-932.

[6] Lin Y, Kang Q, Liu Y, et al. Flexible, highly thermally conductive and electrically insulating phase change materials for advanced thermal management of 5G base stations and thermoelectric generators. Nanomicro Lett. 2023; 15(1): 31.

[7] Zhou T, Liu Y, Cao P, et al. Cold sintered metal–ceramic nanocomposites for high-frequency inductors. Adv Electron Mater. 2020; 6(12).

[8] Raveendran A, Sebastian MT, Raman S. Applications of microwave materials: a review. J Electron Mater. 2019; 48(5): 2601-2634.

[9] Qin J, Liu Z, Ma M, Liu F, Qi ZM, Li Y. Structure and microwave dielectric properties of gillespite-type ACuSi₄O₁₀ (A = Ca, Sr, Ba) ceramics and quantitative prediction of the Q x f value via machine learning. ACS Appl Mater Interfaces. 2021; 13(15): 17817-17826.

[10] Qin J, Liu Z, Ma M, Li Y. Machine learning approaches for permittivity prediction and rational design of microwave dielectric ceramics. J Materiomics. 2021; 7(6): 1284-1293.

[11] Zaki M, Jayadeva KNMA. Interpretable machine learning for understanding compositional and testing condition effects on refractive index, density, dielectric constant, and loss tangent of inorganic melts and glasses. Front Mater. 2024; 11.

[12] Zhao B, Chen X, Chen N, et al. Low-temperature-sintered MgO-based microwave dielectric ceramics with ultralow loss and high thermal conductivity. J Am Ceram Soc. 2022; 106(2): 1159-1169.

[13] Lu Y, Shan Y, Guo X, Yue Z, Zhou H. Enhanced thermal conductivity and mechanical performance of CaO–B₂O₃–SiO₂ glass ceramic with AlN addition for LTCC applications. Ceram Int. 2023; 49(22): 36328-36336.

[14] Gupta R, Kim EY, Shin H.-S, Lee G.-Y, Yeo D.-H. Structural, microstructural, and microwave dielectric properties of (Al_1-xB_x)₂Mo₃O₁₂ ceramics with low dielectric constant and low dielectric loss for LTCC applications. Ceram Int. 2023; 49(14): 22690-22701.

[15] Wu FF, Zhou D, Du C, et al. Design of a sub-6 GHz dielectric resonator antenna with novel temperature-stabilized Sm_1-xBi_xNbO₄ (x = 0-0.15) microwave dielectric ceramics. ACS Appl Mater Interfaces. 2022; 14(5): 7030-7038.

[16] Tian S, Zhou M, Shen HY, et al. Low thermal expansion coefficient LAS glass-ceramics with petalite as the main crystal phase. J Non-Cryst Solids. 2025; 649:123338.

[17] Wang W, Shehbaz M, Wang X, et al. Low-permittivity and low-temperature cofired BaSO₄-BaF₂ microwave dielectric ceramics for high-reliability packaged electronics. ACS Appl Mater Interfaces. 2023; 15(44): 51453-51461.

[18] Guo RZ, Shi RD, Zhu XL, Chen XM. Synergistic modification of properties in Ba[(Zn_0.8Mg_0.2)_1/3Nb_2/3]O₃ ceramics through ordered domain engineering. J Am Ceram Soc. 2023; 106(7): 4275-4283.

[19] Mu N, Chen D, Li B. Influence of Zn/Ba ratio on crystallization, sintering behavior and properties of CaO-Al₂O₃-SiO₂ glass-ceramics. J Non-Cryst Solids. 2023; 622:122662.

[20] Jiang ZH, Zhang QY. The structure of glass: A phase equilibrium diagram approach. Prog Mater Sci. 2014; 61: 144-215.

[21] Wondraczek L, Bouchbinder E, Ehrlicher A, Mauro JC, Sajzew R, Smedskjaer MM. Advancing the mechanical performance of glasses: perspectives and challenges. Adv Mater. 2022; 34(14):e2109029.

[22] Bhattoo R, Bishnoi S, Zaki M, Krishnan NMA. Understanding the compositional control on electrical, mechanical, optical, and physical properties of inorganic glasses with interpretable machine learning. Acta Mater. 2023; 242:118439.

[23] Nakamura K, Otani N, Koike T. Multi-objective Bayesian optimization of optical glass compositions. Ceram Int. 2021; 47(11): 15819-15824.

[24] Zhu J, Ding L, Sun G, Wang L. Accelerating design of glass substrates by machine learning using small-to-medium datasets. Ceram Int. 2024; 50(2): 3018-3025.

[25] Cassar DR, Mastelini SM, Botari T, Alcobaça E, De Carvalho ACPLF, Zanotto ED. Predicting and interpreting oxide glass properties by machine learning using large datasets. Ceram Int. 2021; 47(17): 23958-23972.

[26] Wang Z, Sun Z, Yin H, et al. Data-driven materials innovation and applications. Adv Mater. 2022; 34(36):e2104113.

[27] Qin J, Liu Z, Ma M, Li Y. Optimizing and extending ion dielectric polarizability database for microwave frequencies using machine learning methods. NPJ Comput Mater. 2023; 9(1):132.

[28] Li N, Kang T, Shi Z, Liu Y, Deng T. Unveiling the electronic structures and optical properties of alkaline-earth oxides–modified silicate glasses. Int J Appl Glass Sci. 2022; 14(2): 216-228.

[29] Urata S, Nakamura N, Tada T, Hosono H. Molecular dynamics study on the co-doping effect of Al₂O₃ and fluorine to reduce Rayleigh scattering of silica glass. J Am Ceram Soc. 2021; 104(10): 5001-5015.

[30] Zhao J, Xu X, Chen X, et al. A structure model for phase separated fluoroaluminosilicate glass system by molecular dynamic simulations. J Eur Ceram Soc. 2019; 39(15): 5018-5029.

[31] Shi Z, Arramel A, Bennett TD, Yue Y, Li N. The deformation of short-range order leading to rearrangement of topological network structure in zeolitic imidazolate framework glasses. iScience. 2022; 25(6):104351.

[32] Lu X, Deng L, Du J, Vienna JD. Predicting boron coordination in multicomponent borate and borosilicate glasses using analytical models and machine learning. J Non-Cryst Solids. 2021; 553:120490.

[33] Lu X, Vienna JD, Du J. Glass formulation and composition optimization with property models: a review. J Am Ceram Soc. 2023; 107(3): 1603-1624.

[34] Pan Z, Dellith J, Wondraczek L. Genome mining in glass chemistry using linear component analysis of ion conductivity data. Adv Sci. 2023; 10(21):e2301435.

[35] Bishnoi S, Badge S, Jayadeva KNMA. Predicting oxide glass properties with low complexity neural network and physical and chemical descriptors. J Non-Cryst Solids. 2023; 616:122488.

[36] Salrin TC, Bragatto CB, Wilkinson CJ. Investigating the role of network former interactions on charge carrier diffusivity in glasses. Frontiers in Materials. 2024; 11.

[37] Lundberg SM, Lee SI. A unified approach to interpreting model predictions. In: Conference on Neural Information Processing Systems; 2017. presented at: 31st.

[38] Inglis A, Parnell A, Hurley CB. Visualizing variable importance and variable interaction effects in machine learning models. J Comput Graph Stat. 2022; 31(3): 766-778.

[39] Shi B, Lookman T, Xue D. Multi-objective optimization and its application in materials science. Materials Genome Engineering Advances. 2023; 1(2).

[40] Park T, Kim E, Sun J, Kim M, Hong E, Min K. Rapid discovery of promising materials via active learning with multi-objective optimization. Mater Today Commun. 2023; 37:107245.

[41] Gou W, Shi ZZ, Zhu Y, et al. Multi-objective optimization of three mechanical properties of Mg alloys through machine learning. Materials Genome Engineering Advances. 2024; 2(3).

[42] Łagowska B, Wacławska I, Sitarz M, Szumera M. Spectroscopic studies of structural interactions in silicate-borate-phosphate glass. J Mol Struct. 2018; 1171: 110-116.

[43] Nishi T, Tanaka K, Ohnuma K, et al. Determination of thermal conductivities of B₂O₃-SiO₂ and CaO-B₂O₃-SiO₂ melts. J Nucl Mater. 2018; 510: 193-198.

[44] Stevensson B, Yu Y, Eden M. Structure-composition trends in multicomponent borosilicate-based glasses deduced from molecular dynamics simulations with improved B-O and P-O force fields. Phys Chem Chem Phys. 2018; 20(12): 8192-8209.

[45] Xu XJ, Yue YL, Zhang HT, Du Z. Effect of MgO on structure and properties of CaO-Al₂O₃-SiO₂ glass system. Adv Mater Res. 2011; 306-307: 531-534.

[46] Agathopoulos S, Ferro MC, Xu JY, et al. Structural interpretation of the in vitro reactivity of SiO₂-MgO-Na₂O glasses. Key Eng Mater. 2003; 240-242: 217-220.

[47] Sørensen SS, Johra H, Mauro JC, Bauchy M, Smedskjaer MM. Boron anomaly in the thermal conductivity of lithium borate glasses. Phys Rev Mater. 2019; 3(7):075601.

[48] Liang T, Liu Y, Zheng W, et al. The effect of boron anomaly on the dielectric properties and thermal expansion of barium borosilicate glasses for 3D packaging systems. Ceram Int. 2024; 50(18): 32217-32224.

[49] Ke Z, Cao X, Shan C, et al. The effect of alkali metal oxide on the properties of borosilicate fireproof glass: structure, thermal properties, viscosity, chemical stability. Ceram Int. 2021; 47(14): 19605-19613.

[50] Yao Y, Cao L, Yang H, et al. High-entropy Mg_1.8R_0.2Al₄Si₅O₁₈ (R = Ni, Co, Zn, Cu, Mn) cordierite ceramics: influence of octahedral distortion and electronegativity mismatch on the microwave dielectric properties. Ceram Int. 2024; 50(23): 51826-51831.

[51] Terada M, Kawamura K, Kagomiya I, Kakimoto K.-i, Ohsato H. Effect of Ni substitution on the microwave dielectric properties of cordierite. J Eur Ceram Soc. 2007; 27(8-9): 3045-3048.

[52] Lou W, Mao M, Song K, et al. Low permittivity cordierite-based microwave dielectric ceramics for 5G/6G telecommunications. J Eur Ceram Soc. 2022; 42(6): 2820-2826.

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2025 The Author(s). Materials Genome Engineering Advances published by Wiley-VCH GmbH on behalf of University of Science and Technology Beijing.