Modern kernel models have also been developed in recent years. Inspired by Behler's atomic HDNN approach, Bartók et al. introduced Gaussian Approximation Potentials (GAP) in 2010 for fitting atomic energies with a 4D spherical harmonic atomic descriptor. In 2013, the same group introduced a new type of atomic descriptor named SOAP (Smooth Overlap Atomic Positions) as a similarity measure between atomic neighbor environments. SOAP guarantees faithfulness without restrictions on radials cutoff and is widely applied with GPR models. In 2015, Spectral Neighbor Analysis Potential (SNAP) was developed by Thompson and coworkers for modeling solid and liquid systems . In 2018, Chmiela et al. developed the symmetrized gradient domain machine learning (sGDML) model to directly create a global force field in a data efficient way. Though sGDML can achieve high accuracy in configuration space, it is not transferable to different systems. In addition to kernel-based and NN-based models, recent development of linear and polynomial based models such as atomic cluster expansion (ACE) , moment tensor potentials (MTP) and Chebyshev Interaction Model for Efficient Simulation (ChIMES) are also popular in the development of MLPs.