Neural-network potential energy surface with small database and high precision: A benchmark of the H + H₂ system

To deeply understand the neural-network (NN) fitting procedure in constructing a potential energy surface (PES) in a wide energy range with a rather small database, based on the existing BKMP2 PES of H + H₂, the relationship between NN function features and the size of the database is studied using the multiconfiguration time-dependent Hartree method for quantum dynamics calculations. First, employing 3843, 3843, 2024, and 1448 energy points, four independent NN-PESs are constructed to discuss the relationship among the size of the database, NN functional structure, and fitting accuracy. Dynamics calculations on these different NN PESs give similar reactive probabilities, which indicate that one has to balance the number of energy points for NN training and the number of neurons in the NN function. To explain this problem and try to resolve it, a quantitative model between the data volume and network scale is proposed. Then, this model is discussed and verified through 14 NN PESs fitted using 3843 energy points and various NN functional forms.