Employing the active learning strategy to construct full-dimensional intermolecular potential energy surfaces within spectroscopic accuracy

In this work, we employed an uncertainty-driven active learning strategy to achieve highly efficient point sampling for full-dimension potential energy surface constructions. The model uncertainty is defined as the weighted square energy difference between two neural network (NN) models trained with the same dataset, and the local maximums of uncertainty would be added into 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. The 6-D H$_2$O-He system was chosen as the test system. A reference PES was constructed firstly by the newly developed MLRNet model with a weighted RMSE of 0.028 cm$^{-1}$, where the full-dimension long-range function was fitted by a pruned basis expansion method. Our tests demonstrate that it is also reliable for the long-range switched fundamental invariant neural network (LS-FI-NN) to construct spectroscopically accurate PES, however, it is less inefficient for the newly developed MLRNet model. For the first single-precision sampling, the LS-FI-NN only requires 472 fitting points to achieve a weighted-RMSE of 0.3253 cm$^{-1}$ for 47945 test points. In comparison, the MLRNet requires 652 points to reach a similar accuracy. Notably, the MLRNet demonstrated lower training errors across all sampling cycles and lower test errors in the first few cycles with less trainable parameters, which indicates its potential with an appropriate sampling procedure. For the second double-precision sampling, the LS-FI-NN achieved a test RMSD of 0.0710 cm$^{-1}$ with only 613 points, while the MLRNet can't converge to a given threshold for tens of iterations. The spectroscopic calculations were performed to further validate the accuracy of these PESs. The energy levels of the double precision LS-FI-NN showed great agreement with the reference PES's results, with only 0.0161 cm$^{-1}$ and 0.0044 cm$^{-1}$ average errors for vibrational levels and the band origin shifts.

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