Hybrid Neural Network Model Based on CNN+Transformer for Predicting the Spectral Properties of Multilayer Structures

Abstract

Relevance. Predicting the spectral characteristics of multilayer materials is a key task in photonics, optoelectronics, and materials science, as the accuracy of modeling directly affects the efficiency of technological processes and the performance of functional coatings. Classical numerical methods ensure reliable calculations but become computationally demanding when many parameter variations are required. This motivates the development of hybrid architectures that combine physical modeling with the capabilities of modern neural networks.

Goal. The aim of this work is to develop and investigate a hybrid neural network model based on a CNN+Transformer architecture for predicting the spectral characteristics of multilayer structures, and to evaluate its effectiveness in comparison with classical and alternative neural network methods.

Research methods. Training data were generated using the TMM in the spectral range of 300–800 nm. PCA was applied to optimize spectral representation, reducing the number of spectral points while preserving 98% of the data variance. The neural model integrates convolutional layers for extracting local interference-related features and a transformer block for capturing global dependencies. The training process employed a loss function that combines prediction accuracy with regularization, while model validation was performed on an independent test dataset.

The results. The proposed model demonstrated high predictive accuracy, achieving a determination coefficient of R² = 0.99 and a mean squared error below 4%. A comparison with the CNN+LSTM architecture revealed the advantage of the transformer-based model, which more effectively captures long-range spectral correlations and provides faster inference. The model showed strong agreement with TMM-generated reference data and maintained robustness to noise variations in experimental spectra.

Conclusions. The developed hybrid CNN+Transformer model proved to be an effective tool for predicting the spectral characteristics of multilayer structures. Combining physical modeling with deep neural networks ensures high accuracy, computational speed, and generalization capability. The results highlight the promise of this architecture for fast optical analysis and thin-film structure optimization. Future work may include expanding the training dataset, accounting for nonlinear optical effects, and integrating the model into automated design systems for optical materials.