In Figure , we show the contour plots on the present SE3-ETN PES for the H+ CH4 → H2 + CH3 abstraction reaction along the two reactive coordinates, RH-H and RC-H distances, with all energies in eV relative to the H + CH4 asymptote. The geometry and related energy value of the transition state (TS) for the reaction H+ CH4 → H2 + CH3 in dark is obtained on the SE3-ETN PES, while the value in red is from the UCCSD(T)-F12a/AVTZ ab initio calculation. In summary, the SE3-ETN presents a flexible machine-learning framework for potential energy prediction for polyatomic molecules. The framework provides a reliable estimation of UCCSD(T)-F12a/AVTZ ab initio calculations using a total of 63,041 data points for the PESs of organic molecules with their Cartesian coordinates. The error of the model for constructing the PESs is acceptable to obtain the smooth surface for the molecule CH5 about the reaction H+ CH4 → H2 + CH3. The configuration of the TS about the reaction H+ CH4 → H2 + CH3 is in agreement with the experimental results. The 128 polynomial inputs which are much smaller than PIP-NN and FI-NN are used in SE3-ETN to preserve the energy invariance by the operators (permutation, rotation and translation).