Quantitatively predicting and evaluating the hardness of amorphous ribbons via a deep learning-symbolic regression approach

Amorphous ribbons are applicable across various fields due to their advantageous mechanical, physical, and electromagnetic properties. One such property, Vickers hardness (H_v), is foundational and intimately linked with other properties, which have attracted a growing amount of attention from researchers. However, there is a paucity of a well-performed expression for amorphous ribbons that could quantitatively guide the design of new ones with the desired H_v. In the present study, nine machine learning (ML) algorithms were executed on a dataset previously collected by the authors. By comparing the coefficients of determination (R²) of these algorithms on the test sets, the descriptor ranking of the model with the highest accuracy was obtained. Then, the final expression was successfully explored by utilizing three key descriptors, which was accomplished by synthesizing the R² values, descriptor ranking, and Pearson Correlation Coefficient (PCC) for different feature subsets. Furthermore, the intricate relationship between these features and H_v was elucidated during exploration. The efficacy of this framework may also offer insights into the discovery of other properties of novel amorphous ribbons.