Applying the active learning strategy to the construction of full-dimensional neural network potential energy surfaces: Critical tests in H2O–He spectroscopic calculation

Abstract

An uncertainty-driven active learning strategy was employed to achieve efficient point sampling for full-dimension potential energy surface constructions. Model uncertainty is defined as the weighted square energy difference between two neural network models, and the local maximums of uncertainty would be added to the training set by two criteria. A two-step sampling procedure was introduced to reduce the computational costs of expansive double-precision neural network training. A reference potential energy surface (PES) of the 6-D H2O–He system was constructed first by the MLRNet model with a weighted Root-Mean-Square-Error (RMSE) of 0.028 cm−1. The full-dimension long-range function was fitted by a pruned basis expansion method. The current sampling method is reliable for the long-range switched fundamental invariant neural network (LS-FI-NN) to construct spectroscopically accurate PES, where the single precision model achieves a test set RMSE of 0.3253 cm−1 with 472 fitting points and the double precision model is 0.0710 cm−1 with only 613 points. In comparison, the MLRNet requires 652 points to reach a similar accuracy. However, the MLRNet, with fewer parameters, shows lower training errors across all sampling cycles and lower test errors in the first few cycles, indicating its potential with an appropriate sampling procedure. The spectroscopic calculations were performed to validate the accuracy of PESs. The energy levels of the double precision LS-FI-NN showed great agreement with the reference PES’s results, with only 0.0161 and 0.0044 cm−1 average errors for vibrational levels and the band origin shifts.