Enhancing SchNet-Based Structure Prediction for Doped Clusters via Transfer Learning and Fine-Tuning

Doped clusters regulate their electronic structures and magnetic properties via heteroatoms, optimizing stability and core physicochemical performances to suit practical applications. Accurate structural prediction is a key foundation for elucidating structure-property relationships and advancing industrial applications. Despite the advancements of machine learning (ML) in cluster structure prediction, two key challenges remain: (1) predicting heterogeneous clusters demands massive data and computational resources; (2) the lack of standardized approaches for ML frameworks on heterogeneous clusters hinders the portability and efficiency of ML models. To address these challenges, we propose a method based on the SchNet model─which offers a well-established framework well-suited for physicochemical tasks (e.g., potential energy surface (PES) fitting and cluster dynamics simulations)─and integrate transfer learning into this method. By freezing neural network layers and fine-tuning with a minimal data set, we optimize the model for EuSi_<i>n</i> (<i>n</i> = 3-12) clusters. The data set was constructed via ABCluster and Gaussian, with energy validation performed at the PBEPBE/3-21G//LANL2DZ and PBEPBE/6-311G(d)//SDD levels to ensure diversity and accuracy. The transfer-learned ML model successfully predicts the global minimum structures of EuSi_<i>n</i> (<i>n</i> = 3-12) clusters, matching results from traditional density functional theory calculations. Compared to the original SchNet model, the method reduces computational time by 54.09% and data requirements by 88.89%, demonstrating significant efficiency gains. This work overcomes traditional doped cluster calculation bottlenecks, and provides a paradigm for doped cluster ML studies.