[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

Backend and its version

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Python Version, CUDA Version, GCC Version, LAMMPS Version, etc

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Details

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Reproducible Example, Input Files, and Commands

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Further Information, Files, and Links

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[njzjz-bot]

Thanks for the detailed description. There is not a single universal RMSE threshold for the Deep Wannier (DW) model before using it in DPLR. The tolerance depends on the charge assigned to the Wannier centers, the typical WC displacement, and the accuracy you need for the long-range energy/forces.

That said, I would treat an RMSE of ~0.13 Å with caution, especially if the typical/max ion--WC distance is only ~0.53 Å. This is a relatively large fraction of the signal. It is not automatically unusable, but I would not judge it only from the final DPLR energy/force loss, because the short-range DP part may partially compensate errors on the validation set while the long-range decomposition/transferability is still poor.

Recommended checks:

1. First make sure the labels are smooth and uniquely assigned. For DPLR the DW model represents the displacement from an associated atom to its WC. If the WC assignment jumps between neighboring atoms/bonds, crosses PBC inconsistently, or changes ordering between frames, the DW loss will stay high even with a good network.
2. Compare predicted vs reference WC displacements on an independent test set, separated by atom type/environment. Check not only RMSE, but also outliers and whether the error is systematic.
3. Reconstruct the total dipole/polarization from the predicted WCs and compare with the reference using the same convention/gauge. For periodic solids, compare consistently unwrapped quantities or changes rather than mixing different polarization branches.
4. More directly for DPLR: compute the long-range electrostatic energy and forces using reference WCs and predicted WCs on the same configurations. The difference between these two is a better indicator than the DW RMSE alone.
5. Then train/test the full DPLR model and compare energy/force errors against a standard short-range DP baseline and against the DPLR model using reference WCs if possible. Also check MD stability and structural properties.

For MoS2 specifically, the larger error may indicate that the WCs have more covalent/bond-centered character and are harder to assign to a single atom as a smooth local displacement. DPLR works best when the relevant WCs are localized and can be consistently associated with selected atoms. It is not limited to purely ionic systems in principle, but if the WC assignment is ambiguous or the WCs are not well localized, the current DPLR workflow becomes much less reliable. In that case I would first debug the WC assignment/localization and the physical validation above before relying on the final DPLR model.

So my practical suggestion is: do a small DPLR test, but use it mainly as a diagnostic. If the predicted-vs-reference long-range energy/force errors are significant, continue improving the DW labels/model rather than trusting a compensated DPLR energy/force fit.

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