# Prediction of Bandgap and Key Feature Analysis of Lead-Free Double Perovskite Oxides Based on Deep Learning

## TL;DR

This paper uses deep learning to predict and analyze the bandgap of lead-free double perovskite oxides, offering a faster and more efficient alternative to traditional methods.

## Contribution

The study introduces a high-precision deep learning model for bandgap prediction and identifies key electronic descriptors influencing it.

## Key findings

- The MLP model achieved an R2 score of 0.9311 and low prediction errors for bandgap values.
- SHAP analysis identified five electronic structure descriptors as key factors affecting the bandgap.
- Transformer models are better suited for large-scale sequential predictions, while MLP excels in medium-scale structured data.

## Abstract

Lead-free double perovskites possess the capabilities of wide bandgap control, excellent photoelectric performance, and environmental friendliness. They are an ideal alternative system for addressing the heavy metal toxicity of lead-based perovskites and promoting their large-scale application. Precise control of their bandgap is key to the green transformation of optoelectronic devices. Bandgap, as a key parameter determining the photoelectric properties of materials, has limitations in traditional experimental determination and DFT calculation methods, such as being time consuming, labour intensive, costly, and difficult to achieve high-throughput screening. Deep learning provides an efficient solution to this problem, but current research has issues such as a single-model architecture and poor interpretability, which cannot effectively support bandgap regulation. This study utilised 2367 valid datasets of lead-free double perovskites sourced from the Materials Project database and relevant literature. Following preprocessing steps, including MinMaxScaler normalisation and Pearson correlation coefficient screening, the dataset was divided into a ratio of 7:1:2. The bandgap prediction capabilities of four models—MLP, deep ensemble learning, PINN, and Transformer—were systematically compared, with feature importance analysed using the SHAP method. The results show that the MLP model performs the best in medium-scale, structured feature prediction. The R2 value of the test set is 0.9311, while the MAE, MSE, and RMSE are 0.1915 eV, 0.0975 eV2, and 0.3122 eV, respectively. A total of 98% of the test samples have a prediction error of ≤0.4 eV, highlighting the stability of low bandgap systems. The Transformer is more suitable for large-scale, sequential feature prediction, while the MLP has limited generalisation ability for medium-to-high bandgap systems containing elements such as Si and Mg. The SHAP analysis revealed that the five electronic structure descriptors, such as B_HOMO+ and A_LUMO+, are the key influencing factors of the bandgap. The research results are helpful for the high-precision prediction and mechanism explanation of the bandgap of lead-free double perovskites, providing theoretical support for rational material design, performance optimisation, and bandgap-oriented regulation. They also point out the direction for subsequent model improvement.