Learning Materials Interatomic Potentials via Hybrid Invariant-Equivariant Architectures

TMLR Paper7084 Authors

Abstract: Machine learning interatomic potentials (MLIPs) can predict energy, force, and stress of materials and enable a wide range of downstream discovery tasks. A key design choice in MLIPs involves the trade-off between invariant and equivariant architectures. Invariant models offer computational efficiency but may not perform as well, especially when predicting high-order outputs. In contrast, equivariant models can capture high-order symmetries, but are computationally expensive. In this work, we propose HIENet, a \underline{h}ybrid \underline{i}nvariant-\underline{e}quivariant materials interatomic potential model that integrates both invariant and equivariant message passing layers. Furthermore, we show that HIENet provably satisfies key physical constraints. HIENet achieves superior performance with considerable computational speedups over prior models. Experimental results on both common benchmarks and downstream materials discovery tasks demonstrate the efficiency and effectiveness of HIENet. Finally, additional ablations further demonstrate that our hybrid invariant-equivariant approach scales well across model sizes and works with different equivariant model architectures, providing powerful insights into future MLIP designs.

Submission Type: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission: We have revised the manuscript based on reviewer feedback. Key changes include: (1) moved the Related Work section to immediately after the Introduction; (2) clarified physical constraint violations for EquiformerV2 and ORB in the introduction and related work; (3) moved the O(3) vs. SO(3) graph construction ablation and layer ordering ablation into the main text (Sec. 5.6) with added discussion; (4) softened overly broad claims throughout; (5) added a citation to Fu et al. for the graph construction point; (6) corrected notation $\mathbf{Z} \in \mathbb{Z}^n$; (7) clarified the $\textbf{TP}_\ell$ and $\mathbf{W}\textbf{f}_i$ notation around Eq. 7; (8) added a discussion of recent MLIPs in Appendix E; (9) added an explicit statement about single-run training in the limitations section; and (10) fixed the typographical error in Table 6. (11) Added reference to Appendix E in Table 1 (12) Expanded discussion of recent MLIPs in the Related Works section.

Code: https://github.com/divelab/AIRS/tree/main/OpenMat/HIENet

Assigned Action Editor: ~Chang_Liu10

Submission Number: 7084