Feature engineering via sure independence screening sparifying operator and sparrow search algorithm optimized artificial neural network reveals hardness descriptors for (Nb-Ti-V-Zr)C ceramics

Replacing Nb by other rare metals M (M = V, Ti, W, Mo …) elements to vary the constituents of (Nb,M)C particle for surface modification has been an effective strategy to improve the wear resistance properties of engineering materials. However, due to the extensive X available solute contents and compositions, developing (Nb,M)C is still challenging. Herein, we tried to design quaternary Nb-based ceramics with multiple components including common elements for solid solution: Ti, V and Zr. With a combination of machine learning and virtual crystal approximation scheme, compositional space of predicted hardness for (Nb-Ti-V-Zr)C ceramics was constructed. A novel physical optimization algorithm named sparrow search algorithm (SSA) was first applied to optimize the input parameters including weight values and neuron threshold of back propagation neural network (BPNN). The hardness values of the predicted potential candidates with high hardness from the SSA-BPNN and first principles calculations are close, suggesting high predictive accuracy and good performance of the well-trained SSA-BPNN model. We further discussed the feature importance via introducing approaches from feature engineering including feature filter, feature dimension reduction and feature stability selection methods, and four features that contribute the most to hardness among the features were obtained. We also performed new feature construction by sure independence sparifying screening operator (SISSO) modelling, which was regarded as a more complicated pre-processing method, and two novel features were proposed based on the selected four features with the most significant feature importance.