Data-Efficient Adaptation of DPA-4 Force Fields to DFT+U Energetics: A Case Study in NiO

Technical Summary: Data-Efficient Adaptation of DPA-4 Force Fields to DFT+U Energetics

Problem Statement
Machine-learned force fields (MLFFs) are frequently pretrained on broad materials datasets (e.g., Materials Project, OMat24) that often employ inconsistent electronic-structure conventions. For strongly correlated materials like transition-metal oxides, standard semilocal Density Functional Theory (DFT) often fails to describe localized $d$ electrons and magnetic moments accurately, necessitating corrections like DFT+U. However, mixing datasets generated with and without Hubbard $U$ corrections creates heterogeneous training sets that may lead to non-physical interpolation. Conversely, pretraining exclusively on DFT+U data is computationally expensive and may not be feasible for large-scale foundation models.

A critical open question is whether an MLFF pretrained on a source-level potential energy surface (PES) with qualitatively incorrect phase energetics (e.g., favoring a specific crystal phase due to missing $U$ corrections) can be efficiently adapted to a target-level surface with the correct physics. Specifically, does prior learning of an incorrect energetic preference impede subsequent fine-tuning, or can a compact target dataset reverse a strongly learned bias?

Methodology
The authors use Nickel Oxide (NiO) as a case study to investigate this adaptability. They focus on two competing structural phases: the octahedral (Oct) rocksalt-like phase and the square-planar (Sqr) PdO-like phase.

• Electronic Structure Benchmarking: The study establishes that non-spin-polarized PBE predicts the Sqr phase to be energetically favorable over Oct, whereas spin-polarized PBE+U (with $U_{eff} = 6.2$ eV) and HSE06 predict the opposite ordering (Oct favored). This qualitative reversal provides a stringent test for MLFF adaptation.
• Dataset Generation:
  • Source Data: Ab initio molecular dynamics (AIMD) trajectories were generated for both Oct and Sqr phases using non-spin-polarized PBE and ferromagnetic (FM) PBE+U.
  • Selection: Training configurations were selected from AIMD frames using the QUESTS algorithm to maximize information entropy, ensuring diverse sampling of local atomic environments.
• Model Architecture and Fine-Tuning:
  • Four foundation models were evaluated: DPA-3 (MP and OMat24 branches) and DPA-4 (Air-MP and Neo-OMAT branches).
  • Strategy 1 (Direct Fine-Tuning): Pretrained models were fine-tuned directly on the FM PBE+U dataset.
  • Strategy 2 (Two-Stage Fine-Tuning): Models were first fine-tuned on the non-spin-polarized PBE dataset (encoding the incorrect Sqr-favored preference) and subsequently fine-tuned on the FM PBE+U dataset.
• Evaluation: Performance was measured by root-mean-square errors (RMSE) for energy and forces on held-out test sets, as well as the ability to reproduce the qualitative Oct–Sqr phase ordering along a structural interpolation path.

Key Results

1. Rapid Adaptation to Target Physics: Pretrained DPA-4 models adapted rapidly to the FM PBE+U surface. With only approximately 170 training configurations, the models achieved energy RMSEs of ~0.5 meV/atom and force RMSEs of ~30 meV/Å. This represents a significant reduction from zero-shot errors (15–20 meV/atom for energy).
2. Reversal of Incorrect Energetic Preferences: Crucially, models that were first fine-tuned to the non-spin-polarized PBE surface (which incorrectly favored the Sqr phase) were able to recover the correct PBE+U phase ordering (Oct favored) with nearly the same data efficiency as models fine-tuned directly from their pretrained initialization.
   • The two-stage fine-tuned model correctly predicted the Sqr phase to be higher in energy than Oct by 0.765 eV/f.u., closely matching the direct PBE+U fine-tuning result and the DFT+U reference (0.936 eV/f.u.).
   • This demonstrates that prior learning of a qualitatively incorrect phase preference does not preclude efficient downstream adaptation.
3. Architecture Dependence: DPA-4 models exhibited superior data efficiency and reproducibility compared to DPA-3 models. DPA-3 models required larger training sets to reach similar force RMSEs and showed greater variation across independent fine-tuning runs.
4. Quantitative Limitations: While the qualitative phase ordering was successfully recovered, the magnitude of the energy difference was slightly underestimated. The authors attribute this residual error to uneven coverage in the target dataset, where configurations near the Sqr phase were underrepresented due to AIMD trajectory evolution and electronic convergence issues.

Significance and Claims
The paper argues that foundation MLFFs should be viewed as transferable priors rather than universally accurate zero-shot calculators. The results support a practical multi-fidelity strategy:

• Pretraining: Should prioritize broad configurational coverage, label consistency (e.g., using consistent DFT without $U$ to avoid mixing Hamiltonians), and computational affordability.
• Fine-Tuning: Compact, application-specific datasets at higher-fidelity levels (e.g., DFT+U) can impose the correct electronic and energetic fidelity required for specific correlated materials.

The authors claim that incorrect source-level phase energetics do not render a pretrained MLFF unsuitable for target-level adaptation. Instead, the ability to efficiently reverse strong energetic biases with limited target data is a critical criterion for evaluating the utility of foundation MLFFs. This approach allows for the use of large, consistent, and affordable datasets for pretraining while relying on targeted fine-tuning to resolve material-specific physics, such as strong correlation effects.