In Figure , we introduce that the node information of the molecular graph is the atomic information. One hot vector is used to describe the atomic types. For the edge information, we use the full-connected format and district different edges C-H and H-H with different one-hot vectors. We use the attention method to embed the graph features and the 3-dimensional coordinates information into the network. The mean absolute error (MAE) is defined as the loss function in the SE3-transformer training for the ab initio potential energies. The prediction potential energies are calculated by linear network functions and activation functions on the final updated features in this work. The six-atomic molecule (CH5) database which was computed at the UCCSD(T)-F12a/AVTZ level, was used in this work with a total of 63,041 data points. In this work, the data points are randomly divided into training, validation, and testing set by the proportions of 95%/2.5%/2.5%. The root mean squared errors (RMSEs) are calculated to compare with previous network fitting. The results of MAEs and RMSEs for the total, training, validation, and testing are listed in Table . The accuracy of the SE3-transformer model in potential energy surface fitting is in agreement with the previous FI-NN fitting. The difference between the SE3transformer model and FINN is that the former uses the Cartesian coordinates and the SE3 equivariance but the latter uses the internal coordinates and the fundamental invariance. For describing the permutation invariance, the fundamental invariance number will be rapidly increasing following the atom number, and the same atom number increase. The hyperparameters of the SE3-transformer model are optimized to obtain this network in Table . Compared with the PIP-NN and FI-NN, the polynomial inputs of SE3-ETN are obtained by a network for the multilayer perceptron (MLP). The number of the polynomial inputs can be smaller than the PIP-NN and FI-NN to obtain the good behavior that the permutation invariance of configurations can be used for fitting the potential energy in the CH5 molecular system. In Table , the numbers of polynomial inputs are illustrated that 128 polynomial inputs of SE3-ETN are much smaller than PIP-NN and FI-NN. The number of polynomial inputs for SE3-ETN are related to the number of channels and the degrees in the SE3-transformer process. The errors of total potential values are shown in Figure (a), and Figures , indicating the performance of the total points for predicting potential energies against the ab initio values. The total MAE as a function of training epochs for predicting potential energies is shown in Figure . A decrease of the MAE of the predicted values compared with a couple of cluster calculated values for both different training sets as the number of training steps is increased. The total, training, validation, and test MAEs of the final network after 100 epochs are no more than 5 meV, which is accuracy for the PESs fitting. The distribution of the absolute fitting errors for the numbers of the selected points is shown in Figure .