Introduction. Machine learning (ML) has been widely used for material modeling with a balance of speed and accuracy in recent years . The computational cost can be greatly reduced compared with ab initio calculation, leading to feasible simulations of large systems . Most ML models for materials are built with kernel-based ML algorithms which use the descriptors of materials as the input and learn the mapping function between the input descriptor and the material's corresponding energy, such as kernel ridge regression (KRR) and gaussian process regression (GPR) methods. A large variety of descriptors have been developed to encode the material information .