Node transfer for multi-fidelity and multimodal machine learning for predicting experimental bandgaps

Bandgap is a key property of materials. In recent years, machine learning has become a powerful tool to predict the experimental bandgaps of compounds before synthesis, but there is still much room for improving the prediction accuracy. Here, we build a machine learning framework that consists of multi-fidelity and multimodal learning models to integrate heterogeneous data sources obtained from first-principle calculations and x-ray diffraction spectra. A new information-fusion strategy named node transfer is proposed. Compared to the widely used Δ-learning strategy, it naturally extends two-fidelity to multi-fidelity learning and facilitates heterogeneous multimodal integration. Node transfer consistently outperforms Δ-learning across two-fidelity, multi-fidelity, and multimodal benchmarks under fine-tuning. The best model involves XRD-based descriptors and encoded descriptors pre-trained based on four computational datasets using different functionals. It achieves a mean absolute error of 0.258 eV, a 26.3% reduction vs the single-fidelity baseline of 0.350 eV. In all prediction tasks, only the chemical composition of the crystal is required as input for the constructed machine learning models, which is free of structural information and, therefore, applicable to materials design before experiments or first-principle calculations.