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<p>Predicting the refractive index (<i>n</i>) of oxide glass is essential for evaluating its optical quality. Traditional prediction methods often struggle to capture the complex relationship between a glass’s chemical composition and its optical properties due to the high dimensionality and sparsity of oxide glass formulations. This study introduces DualNet, a novel dual neural network approach that integrates a U-Net architecture with an Artificial Neural Network (ANN). The U-Net enhances feature extraction by leveraging hierarchical learning, skip connections, and optimized convolutions, improving both generalization and computational efficiency. Meanwhile, the ANN leverages the latent space representations extracted by the U-Net to predict the Refractive Index of Oxide Glasses, utilizing a hybrid loss function to enhance model performance and prediction accuracy. This integrated approach not only extract the low- and high-level spatial features through hierarchical learning and skip connections, while ANN leverages these rich features for precise predictions. The performance of the DualNet is assessed utilising various evaluation metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Median Absolute Error (MedAE), R<sup>2</sup>, and compared with state-of-the-art algorithms, including Support Vector Regression (SVR), Decision Tree Regression, Random Forest Regression, K-Nearest Neighbours (KNN) Regression, and XGBoost Regression. DualNet outperforms all competing algorithms, with up to 66.67% improvement in MSE, 31.73% in RMSE, and 28.64% in MAE, particularly over Decision Tree and KNN. It also achieves the highest R<sup>2</sup> improvement (11.49%), proving its superior predictive accuracy and robustness. Finally, the DualNet achieved high accuracy with a 95% Confidence Interval (CI), demonstrating excellent performance across all metrics: MSE (0.00018–0.00022), RMSE (0.0165–0.0175), MAE (0.0142–0.0152), MedAE (0.0135–0.0147), and R<sup>2</sup> (0.96–0.98). DualNet offers enhanced accuracy and reliability in predicting the refractive index of oxide glasses, making it valuable to design and accelerates cost-effective development of high-performance materials.</p>

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Prediction of oxide glass refractive index using a novel deep learning architecture, DualNet (U-Net and ANN) with hybrid loss function

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • Muhammad Zubair,
  • Ahmad Abubakar Suleiman,
  • Arsalaan Khan Yousafzai,
  • Talal Alazemi

摘要

Predicting the refractive index (n) of oxide glass is essential for evaluating its optical quality. Traditional prediction methods often struggle to capture the complex relationship between a glass’s chemical composition and its optical properties due to the high dimensionality and sparsity of oxide glass formulations. This study introduces DualNet, a novel dual neural network approach that integrates a U-Net architecture with an Artificial Neural Network (ANN). The U-Net enhances feature extraction by leveraging hierarchical learning, skip connections, and optimized convolutions, improving both generalization and computational efficiency. Meanwhile, the ANN leverages the latent space representations extracted by the U-Net to predict the Refractive Index of Oxide Glasses, utilizing a hybrid loss function to enhance model performance and prediction accuracy. This integrated approach not only extract the low- and high-level spatial features through hierarchical learning and skip connections, while ANN leverages these rich features for precise predictions. The performance of the DualNet is assessed utilising various evaluation metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Median Absolute Error (MedAE), R2, and compared with state-of-the-art algorithms, including Support Vector Regression (SVR), Decision Tree Regression, Random Forest Regression, K-Nearest Neighbours (KNN) Regression, and XGBoost Regression. DualNet outperforms all competing algorithms, with up to 66.67% improvement in MSE, 31.73% in RMSE, and 28.64% in MAE, particularly over Decision Tree and KNN. It also achieves the highest R2 improvement (11.49%), proving its superior predictive accuracy and robustness. Finally, the DualNet achieved high accuracy with a 95% Confidence Interval (CI), demonstrating excellent performance across all metrics: MSE (0.00018–0.00022), RMSE (0.0165–0.0175), MAE (0.0142–0.0152), MedAE (0.0135–0.0147), and R2 (0.96–0.98). DualNet offers enhanced accuracy and reliability in predicting the refractive index of oxide glasses, making it valuable to design and accelerates cost-effective development of high-performance materials.