For general E(3) neural networks potential with a vector field without considering time-reversal symmetry, its invariance of energy is preserved with a requirement that the vector field share the same E(3) symmetry with 𝑟 ⃗. However, there is a violation of parity and time-reversal symmetry of 𝑟 ⃗ and 𝑠 ⃗. For example, if we include spin as a vector field of the E(3) model, time-reversal symmetry will break as 𝐸(𝑟 ⃗, 𝑠 ⃗) is not equal to 𝐸(𝑟 ⃗, -𝑠 ⃗) shown in Figure . Though the time-reversal invariance of the energy can be reached by taking the average energy of 𝐸(𝑟 ⃗, 𝑠 ⃗) and 𝐸(𝑟 ⃗, -𝑠 ⃗), it doubles up the consumption of the model on time and memory meanwhile. As a result, it is not an efficient and ideal approach to treat 𝑠 ⃗ as a vector field in E(3) potentials.