As the test RMSE and the corresponding train RMSE in figure become close to each other, we can see the limitation of the single-precision sampling. The only way to further improve the accuracy is by increasing the fitting accuracy during each sampling cycle. As mentioned in Section 2, we will employ the double-precision sampling of which the initial set is the final training set in the single-precision sampling. Figure plots the maximum uncertainty and the train/test RMSE of the FI-NN models. Even in the first iteration of the doubleprecision sampling, the maximum uncertainty and the test set w-RMSE are lower than the final results of the single-precision sampling. Only 11 iterations are enough to reach the stop threshold (0.5 cm -2 ) with 613 fitting points. The final model achieved a test w-RMSE of 0.0710 cm -1 . Although it is possible to further improve the accuracy by setting U stop , we simply stop using this model for spectroscopic calculation because the test w-RMSE is already much better than the previous multi-dimensional MLR result 42 (about 0.1 cm -1 for vibrationally averaged grids).