perparameters to control the behavior of fitting . They can achieve high accuracy for particular chemical systems with very small amounts of data, and have the intrinsic ability to predict variance, which is useful in uncertainty estimations . However, the computational cost of kernel-based methods scales poorly with the size of the dataset, due to the need to compute the inverse of a large covariance matrix . On the other hand, NNs belong to the family of parametric methods, where the number of parameters is fixed at the start of the process. For small molecular systems, they usually require more training data points to achieve the same level of accuracy as kernel-based methods . But the training cost of NNs scales linearly with the size of the dataset, much better than kernel-based methods. Therefore, GPR/KRR are often applied when high accuracy is required with a small amount of data points, such as spectroscopy prediction , while NNs are able to handle millions of data points readily . Recent reviews extensively discussed the progress in the development of NN s and GPR models . Some popular ML models applied in reactive systems are discussed below and organized in Figure . . While PIP-NNs have been successful in small molecular and reactive systems , their applicability to large systems is limited by the rapidly increasing size of PIP inputs as the system size grows.