[Q&A] Recommended Deep Wannier accuracy before using the model in DPLR

[CoderQK]

Question

Hi,

I am trying to train a Deep Potential Long-Range (DPLR) model for a MoS2 system, and I would like to ask about the required accuracy of the Deep Wannier model before using it in the subsequent DPLR workflow.

The reference Wannier centers were generated using the localization functionality in CP2K, with the OT method enabled. I then constructed the Deep Wannier labels by assigning Wannier centers to selected atoms and training the Deep Wannier model to predict the corresponding atomic dipole / Wannier centroid displacement labels.

In my current tests, the Deep Wannier training LOSS decreases only to about RMSE = 0.13 for the atomic dipole labels. I have tried different Wannier-center assignment schemes and different datasets, but the RMSE remains at a similar level. Therefore, I would like to understand whether this level of accuracy is sufficient for building a reliable DPLR model.

As a comparison, I also tested a more ionic Ga2O3 system. In my current analysis, the maximum ion-to-Wannier-centroid distance is about 0.53 Å for MoS2, and the corresponding Deep Wannier loss/RMSE is about 0.13. In contrast, for Ga2O3, the maximum ion-to-Wannier-centroid distance is only about 0.028 Å, and the corresponding loss is about 0.002. This difference makes me wonder whether the larger Deep Wannier error in MoS2 is still acceptable for DPLR, or whether it indicates that the current WC assignment / Deep Wannier model is not accurate enough.

My main questions are:

1. Is there a recommended accuracy threshold for the Deep Wannier model before it is used in DPLR? For example, should the RMSE be below a certain value in Å, or should it be judged relative to the typical magnitude of the atomic dipole labels?

2. If the Deep Wannier RMSE remains around 0.1 after testing different WC assignment schemes and datasets, would you recommend continuing to improve the Deep Wannier model first, or is it reasonable to proceed with DPLR training and evaluate the final reliability from the DPLR energy and force errors?

3. Besides the Deep Wannier validation RMSE, what additional quantities should be checked to determine whether the predicted Wannier centroids are accurate enough for DPLR? For example, should one compare dipole moments, polarization, long-range electrostatic energies, or long-range electrostatic forces with reference data?

4. For condensed-phase or solid-state systems, is the current DPLR framework mainly suitable for systems with highly localized Wannier centers, such as ionic crystals? Are there any known limitations or recommended practices when applying DPLR to materials with more covalent bonding character, such as MoS2?

Thanks very much!

DeePMD-kit Version

3.1.3

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