journal article·2025-02-26Open access

Efficient equivariant model for machine learning interatomic potentials

Ziduo Yang, Xian Wang, Yifan Li, Qiujie Lv, Calvin Yu-Chian Chen, Lei Shen

npj Computational Materials· Volume 11· Issue 1

Abstract

In modern computational materials, machine learning has shown the capability to predict interatomic potentials, thereby supporting and accelerating conventional molecular dynamics (MD) simulations. However, existing models typically sacrifice either accuracy or efficiency. Moreover, efficient models are highly demanded for offering simulating systems on a considerably larger scale at reduced computational costs. Here, we introduce an efficient equivariant graph neural network (E 2 GNN) that can enable accurate and efficient interatomic potential and force predictions for molecules and crystals. Rather than relying on higher-order representations, E 2 GNN employs a scalar-vector dual representation to encode equivariant features. By learning geometric symmetry information, our model remains efficient while ensuring prediction accuracy and robustness through the equivariance. Our results show that E 2 GNN consistently outperforms the prediction performance of the representative baselines and achieves significant efficiency across diverse datasets, which include catalysts, molecules, and organic isomers. Furthermore, we conduct MD simulations using the E 2 GNN force field across solid, liquid, and gas systems. It is found that E 2 GNN can achieve the accuracy of ab initio MD across all examined systems.
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Research context

OpenAlex topics: Machine Learning in Materials Science · Computational Drug Discovery Methods · Nuclear Materials and Properties

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (44)

Show source-provided references
1. Batatia, I., Kovacs, D. P., Simm, G., Ortner, C. & Csányi, G. Mace: Higher order equivariant message passing neural networks for fast and accurate force fields. Adv. Neural Inf. Process. Syst. 35, 11423–11436 (2022).
2. Batzner, S. et al. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun. 13, 2453 (2022).10.1038/s41467-022-29939-5 ↗
3. Chen, C. & Ong, S. P. A universal graph deep learning interatomic potential for the periodic table. Nat. Comput. Sci. 2, 718–728 (2022).10.1038/s43588-022-00349-3 ↗
4. Xie, F., Lu, T., Meng, S. & Liu, M. Gptff: A high-accuracy out-of-the-box universal ai force field for arbitrary inorganic materials. Sci. Bulletin 69, 3525–3532 (2024).10.1016/j.scib.2024.08.039 ↗
5. Zhong, Y., Yu, H., Su, M., Gong, X. & Xiang, H. Transferable equivariant graph neural networks for the Hamiltonians of molecules and solids. npj Comput. Mater. 9, 182 (2023).10.1038/s41524-023-01130-4 ↗
6. Zhong, Y. et al. Universal machine learning Kohn-sham Hamiltonian for materials. Chin. Phys. Lett. 41, 077103 (2024).10.1088/0256-307X/41/7/077103 ↗
7. Li, H. et al. Deep-learning density functional theory Hamiltonian for efficient ab initio electronic-structure calculation. Nat. Comput. Sci. 2, 367–377 (2022).10.1038/s43588-022-00265-6 ↗
8. Wang, Y. et al. Universal materials model of deep-learning density functional theory Hamiltonian. Sci. Bull. 69, 2514–2521 (2024).10.1016/j.scib.2024.06.011 ↗
9. Zhang, L., Han, J., Wang, H., Car, R. & E, W. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120, 143001 (2018).10.1103/PhysRevLett.120.143001 ↗
10. Yoon, J. & Ulissi, Z. W. Differentiable optimization for the prediction of ground state structures (dogss). Phys. Rev. Lett. 125, 173001 (2020).10.1103/PhysRevLett.125.173001 ↗
11. Deng, B. et al. Chgnet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nat. Machine Intell. 1–11 (2023).10.1038/s42256-023-00716-3 ↗
12. Pablo-García, S. et al. Fast evaluation of the adsorption energy of organic molecules on metals via graph neural networks. Nat. Comput. Sci. 1–10 (2023).10.26434/chemrxiv-2022-m719x ↗
13. Li, Y. et al. Local environment interaction-based machine learning framework for predicting molecular adsorption energy. J. Mater. Inform. 4, 4 (2024).
14. Dai, M., Demirel, M. F., Liang, Y. & Hu, J.-M. Graph neural networks for an accurate and interpretable prediction of the properties of polycrystalline materials. npj Comput. Mater. 7, 103 (2021).10.1038/s41524-021-00574-w ↗
15. Hu, W. et al. Forcenet: a graph neural network for large-scale quantum calculations. arXiv preprint arXiv:2103.01436.
16. Xie, T. & Grossman, J. C. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett. 120, 145301 (2018).10.1103/PhysRevLett.120.145301 ↗
17. Schütt, K. et al. Schnet: a continuous-filter convolutional neural network for modeling quantum interactions. Adv. Neural Inf. Process. Syst. 30, 1–11 (2017).
18. Chen, C., Ye, W., Zuo, Y., Zheng, C. & Ong, S. P. Graph networks as a universal machine learning framework for molecules and crystals. Chem. Mater. 31, 3564–3572 (2019).10.1021/acs.chemmater.9b01294 ↗
19. Choudhary, K. & DeCost, B. Atomistic line graph neural network for improved materials property predictions. npj Comput. Mater. 7, 185–192 (2021).10.1038/s41524-021-00650-1 ↗
20. Han, J. et al. A survey of geometric graph neural networks: Data structures, models and applications. arXiv preprint arXiv:2403.00485.
21. Gong, X. et al. General framework for e(3)-equivariant neural network representation of density functional theory Hamiltonian. Nat. Commun. 14, 2848 (2023).10.1038/s41467-023-38468-8 ↗
22. Fuchs, F., Worrall, D., Fischer, V. & Welling, M. Se(3)-transformers: 3d roto-translation equivariant attention networks. Adv. Neural Inf. Process. Syst. 33, 1970–1981 (2020).
23. Brandstetter, J., Hesselink, R., van der Pol, E., Bekkers, E. J. & Welling, M. Geometric and physical quantities improve e(3) equivariant message passing. In: Proc. International Conference on Learning Representations (2021).
24. Satorras, V. G., Hoogeboom, E. & Welling, M. E(n) equivariant graph neural networks. In: Proc. International Conference on Machine Learning, pp. 9323–9332 (2021).
25. Zitnick, C. L. et al. Spherical channels for modeling atomic interactions. In: Advances in Neural Information Processing Systems (NeurIPS) (2022).
26. Passaro, S. & Zitnick, C. L. Reducing so (3) convolutions to so (2) for efficient equivariant gnns. In: International Conference on Machine Learning, pp. 27420–27438 (2023).
27. Yang, Z. et al. Scalable crystal structure relaxation using an iteration-free deep generative model with uncertainty quantification. Nat. Commun. 15, 8148 (2024).10.1038/s41467-024-52378-3 ↗
28. Gasteiger, J., Groß, J. & Günnemann, S. Directional message passing for molecular graphs. In: Proc. International Conference on Learning Representations (ICLR) (2020).
29. Gasteiger, J., Becker, F. & Günnemann, S. Gemnet: Universal directional graph neural networks for molecules. Adv. Neural Inf. Process. Syst. 34, 6790–6802 (2021).
30. Liu, Y. et al. Spherical message passing for 3d molecular graphs. In: International Conference on Learning Representations (ICLR) (2022).
31. Atz, K., Grisoni, F. & Schneider, G. Geometric deep learning on molecular representations. Nat. Mach. Intell. 3, 1023–1032 (2021).10.1038/s42256-021-00418-8 ↗
32. Shuaibi, M. et al. Rotation invariant graph neural networks using spin convolutions. arXiv preprint arXiv:2106.09575.
33. Batzner, S., Musaelian, A. & Kozinsky, B. Advancing molecular simulation with equivariant interatomic potentials. Nat. Rev. Phys., 1–2 (2023).10.1038/s42254-023-00615-x ↗
34. Musaelian, A. et al. Learning local equivariant representations for large-scale atomistic dynamics. Nat. Commun. 14, 579 (2023).10.1038/s41467-023-36329-y ↗
35. Batatia, I., Schaaf, L. L., Csanyi, G., Ortner, C. & Faber, F. A. Equivariant matrix function neural networks. In: The Twelfth International Conference on Learning Representations (2024).
36. Fu, X. et al. Forces are not enough: benchmark and critical evaluation for machine learning force fields with molecular simulations. Trans. Mach. Learn. Res. (2023).
37. Schütt, K., Unke, O. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. In: Proc. International Conference on Machine Learning, pp. 9377–9388 (2021).
38. Haghighatlari, M. et al. Newtonnet: Newtonian message passing network for deep learning of interatomic potentials and forces. Digit. Discov. 1, 333–343 (2022).10.1039/D2DD00008C ↗
39. Park, C. W. et al. Accurate and scalable graph neural network force field and molecular dynamics with direct force architecture. npj Comput. Mater. 7, 73 (2021).10.1038/s41524-021-00543-3 ↗
40. Chanussot, L. et al. Open catalyst 2020 (oc20) dataset and community challenges. ACS Catal. 11, 6059–6072 (2021).10.1021/acscatal.0c04525 ↗
41. Tran, R. et al. The open catalyst 2022 (oc22) dataset and challenges for oxide electrocatalysts. ACS Catal. 13, 3066–3084 (2023).10.1021/acscatal.2c05426 ↗
42. Gasteiger, J., Giri, S., Margraf, J. T. & Günnemann, S. Fast and uncertainty-aware directional message passing for non-equilibrium molecules. In: Proc. Machine Learning for Molecules Workshop, NeurIPS (2020).
43. Kolluru, A. et al. Open challenges in developing generalizable large-scale machine-learning models for catalyst discovery. ACS Catal. 12, 8572–8581 (2022).10.1021/acscatal.2c02291 ↗
44. Zhang, L. et al. End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems. Adv. Neural Inf. Process. Syst. 31 (2018).