- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Convolutional neural networks enable high-fidelity prediction of rotation-invariant properties of amorphous and crystalline materials

Zhao Fan*

  • *Contact author: zfan2016@gmail.com
PDF

Phys. Rev. Materials 10, 053803 – Published 14 May, 2026

DOI: https://doi.org/10.1103/x3fw-pjcf

Abstract

Over the past two decades, various machine learning (ML) methods have been broadly used to predict properties from structure of materials, which is valuable in accelerating the discovery and development of new materials for different applications. Convolutional neural networks (CNN), however, have not been widely used in materials science, although they have been demonstrated to possess the state-of-the-art learning capability in the field of computer vision and pattern recognition. Recently, it was shown that CNN are powerful in predicting orientation-dependent properties when using a new structure representation—spatial density map (SDM). However, it is unclear whether the deep learning (DL) framework combining CNN and SDM is useful for predicting rotation-invariant properties because of the lack of rotational invariance of SDMs. Here, we demonstrate that this DL framework can also enable high-fidelity prediction of rotation-invariant properties through two examples, i.e., predicting the flexibility volume of metallic glasses and the grain-boundary segregation energy of polycrystals. This is realized through training CNN models via data augmentation and defining a common protocol to establish a unique local coordinate system to compute SDMs when applying CNN models. The advantages of the DL framework arise from the completeness of the SDM and the excellent learning capability of CNN models. Thanks to the high fidelity of CNN models, additional physical insights into structure–property relationships are obtained. The DL method is expected to be useful for a broad range of topics in materials science.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (81)

  1. D. Morgan and R. Jacobs, Opportunities and challenges for machine learning in materials science, Annu. Rev. Mater. Res. 50, 71 (2020).
  2. K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, Machine learning for molecular and materials science, Nature (London) 559, 547 (2018).
  3. J. Schmidt, M. R. G. Marques, S. Botti, and M. A. L. Marques, Recent advances and applications of machine learning in solid-state materials science, npj Comput. Mater. 5, 83 (2019).
  4. A. V. Shapeev, Moment tensor potentials: A class of systematically improvable interatomic potentials, Multiscale Model. Simul. 14, 1153 (2016).
  5. A. Bochkarev, Y. Lysogorskiy, and R. Drautz, Graph atomic cluster expansion for semilocal interactions beyond equivariant message passing, Phys. Rev. X 14, 021036 (2024).
  6. P. Friederich, F. Häse, J. Proppe, and A. Aspuru-Guzik, Machine-learned potentials for next-generation matter simulations, Nat. Mater. 20, 750 (2021).
  7. J. Behler and M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett. 98, 146401 (2007).
  8. A. P. Bartók, M. C. Payne, R. Kondor, and G. Csányi, Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons, Phys. Rev. Lett. 104, 136403 (2010).
  9. L. Zhang, J. Han, H. Wang, R. Car, and W. E., Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics, Phys. Rev. Lett. 120, 143001 (2018).
  10. R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B 99, 014104 (2019).
  11. H. W. Chung, R. Freitas, G. Cheon, and E. J. Reed, Data-centric framework for crystal structure identification in atomistic simulations using machine learning, Phys. Rev. Mater. 6, 043801 (2022).
  12. G. M. Coli and M. Dijkstra, An artificial neural network reveals the nucleation mechanism of a binary colloidal AB13 crystal, ACS Nano 15, 4335 (2021).
  13. P. Geiger and C. Dellago, Neural networks for local structure detection in polymorphic systems, J. Chem. Phys. 139, 164105 (2013).
  14. S. De, A. P. Bartók, G. Csányi, and M. Ceriotti, Comparing molecules and solids across structural and alchemical space, Phys. Chem. Chem. Phys. 18, 13754 (2016).
  15. C. Dietz, T. Kretz, and M. H. Thoma, Machine-learning approach for local classification of crystalline structures in multiphase systems, Phys. Rev. E 96, 011301(R) (2017).
  16. E. Boattini, M. Ram, F. Smallenburg, and L. Filion, Neural-network-based order parameters for classification of binary hard-sphere crystal structures, Mol. Phys. 116, 3066 (2018).
  17. A. Ziletti, D. Kumar, M. Scheffler, and L. M. Ghiringhelli, Insightful classification of crystal structures using deep learning, Nat. Commun. 9, 2775 (2018).
  18. A. Leitherer, A. Ziletti, and L. M. Ghiringhelli, Robust recognition and exploratory analysis of crystal structures via Bayesian deep learning, Nat. Commun. 12, 6234 (2021).
  19. R. S. DeFever, C. Targonski, S. W. Hall, M. C. Smith, and S. Sarupria, A generalized deep learning approach for local structure identification in molecular simulations, Chem. Sci. 10, 7503 (2019).
  20. S. Hong, K. Nomura, A. Krishnamoorthy, P. Rajak, C. Sheng, R. K. Kalia, A. Nakano, and P. Vashishta, Defect healing in layered materials: A machine learning-assisted characterization of MoS2 crystal phases, J. Phys. Chem. Lett. 10, 2739 (2019).
  21. Q. Wang, L.-F. Zhang, Z.-Y. Zhou, and H.-B. Yu, Predicting the pathways of string-like motions in metallic glasses via path-featurizing graph neural networks, Sci. Adv. 10, eadk2799 (2024).
  22. E. D. Cubuk, S. S. Schoenholz, J. M. Rieser, B. D. Malone, J. Rottler, D. J. Durian, E. Kaxiras, and A. J. Liu, Identifying structural flow defects in disordered solids using machine-learning methods, Phys. Rev. Lett. 114, 108001 (2015).
  23. Q. Wang and A. Jain, A transferable machine-learning framework linking interstice distribution and plastic heterogeneity in metallic glasses, Nat. Commun. 10, 5537 (2019).
  24. V. Bapst, T. Keck, A. Grabska-Barwińska, C. Donner, E. D. Cubuk, S. S. Schoenholz, A. Obika, A. W. R. Nelson, T. Back, D. Hassabis, and P. Kohli, Unveiling the predictive power of static structure in glassy systems, Nat. Phys. 16, 448 (2020).
  25. Z. Fan, J. Ding, and E. Ma, Machine learning bridges local static structure with multiple properties in metallic glasses, Mater. Today 40, 48 (2020).
  26. Q. Wang, J. Ding, L. Zhang, E. Podryabinkin, A. Shapeev, and E. Ma, Predicting the propensity for thermally activated β events in metallic glasses via interpretable machine learning, npj Comput. Mater. 6, 194 (2020).
  27. C. W. Rosenbrock, E. R. Homer, G. Csányi, and G. L. W. Hart, Discovering the building blocks of atomic systems using machine learning: Application to grain boundaries, npj Comput. Mater. 3, 29 (2017).
  28. M. Wagih and C. A. Schuh, Learning grain-boundary segregation: From first principles to polycrystals, Phys. Rev. Lett. 129, 046102 (2022).
  29. M. Wagih, P. M. Larsen, and C. A. Schuh, Learning grain boundary segregation energy spectra in polycrystals, Nat. Commun. 11, 6376 (2020).
  30. N. Tuchinda and C. A. Schuh, Grain size dependencies of intergranular solute segregation in nanocrystalline materials, Acta Mater. 226, 117614 (2022).
  31. Z. Zhang and C. Deng, Grain boundary interstitial segregation in substitutional binary alloys, Acta Mater. 291, 121019 (2025).
  32. F. Musil, A. Grisafi, A. P. Bartók, C. Ortner, G. Csányi, and M. Ceriotti, Physics-inspired structural representations for molecules and materials, Chem. Rev. 121, 9759 (2021).
  33. M. F. Langer, A. Goeßmann, and M. Rupp, Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning, npj Comput. Mater. 8, 41 (2022).
  34. J. Damewood, J. Karaguesian, J. R. Lunger, A. R. Tan, M. Xie, J. Peng, and R. Gómez-Bombarelli, Representations of materials for machine learning, Annu. Rev. Mater. Res. 53, 399 (2023).
  35. C. T. Cai, A. J. Parker, and A. S. Barnard, Graph representation of multi-dimensional materials, J. Phys. Mater. 7, 022005 (2024).
  36. S. N. Pozdnyakov, M. J. Willatt, A. P. Bartók, C. Ortner, G. Csányi, and M. Ceriotti, Incompleteness of atomic structure representations, Phys. Rev. Lett. 125, 166001 (2020).
  37. K. He, X. Zhang, S. Ren, and J. Sun, Deep residual learning for image recognition, in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, Las Vegas, NV, 2016), pp. 770–778.
  38. Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature (London) 521, 436 (2015).
  39. A. Krizhevsky, I. Sutskever, and G. E. Hinton, Imagenet classification with deep convolutional neural networks, in Advances in Neural Information Processing Systems, edited by F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger, (Curran Associates, Inc., Red Hook, NY, 2012), Vol. 25, pp. 1097–1105.
  40. K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, arXiv:1409.1556.
  41. O. Russakovsky et al., Imagenet large scale visual recognition challenge, Int. J. Comput. Vis. 115, 211 (2015).
  42. M. Ziatdinov, A. Ghosh, C. Y. (Tommy) Wong, and S. V. Kalinin, AtomAI framework for deep learning analysis of image and spectroscopy data in electron and scanning probe microscopy, Nat. Mach. Intell. 4, 1101 (2022).
  43. K. Kaufmann, C. Zhu, A. S. Rosengarten, D. Maryanovsky, T. J. Harrington, E. Marin, and K. S. Vecchio, Crystal symmetry determination in electron diffraction using machine learning, Science 367, 564 (2020).
  44. M. Ziatdinov, O. Dyck, A. Maksov, X. Li, X. Sang, K. Xiao, R. R. Unocic, R. Vasudevan, S. Jesse, and S. V. Kalinin, Deep learning of atomically resolved scanning transmission electron microscopy images: Chemical identification and tracking local transformations, ACS Nano 11, 12742 (2017).
  45. X. Zhou, Y. Wei, M. Kühbach, H. Zhao, F. Vogel, R. Darvishi Kamachali, G. B. Thompson, D. Raabe, and B. Gault, Revealing in-plane grain boundary composition features through machine learning from atom probe tomography data, Acta Mater. 226, 117633 (2022).
  46. Z. Fan and E. Ma, Predicting orientation-dependent plastic susceptibility from static structure in amorphous solids via deep learning, Nat. Commun. 12, 1506 (2021).
  47. Z. Fan, E. Ma, and M. L. Falk, Predicting the location of shear band initiation in a metallic glass, Phys. Rev. Mater. 6, 065602 (2022).
  48. Z. Fan, B. Xing, and P. Cao, Predicting path-dependent diffusion barrier spectra in vast compositional space of multi-principal element alloys via convolutional neural networks, Acta Mater. 237, 118159 (2022).
  49. H. Fan, Z. Fan, X. Liu, Z. Lu, and E. Ma, Atomic vibration as an indicator of the propensity for configurational rearrangements in metallic glasses, Mater. Horizons 8, 2359 (2021).
  50. J. Ding, Y.-Q. Cheng, H. Sheng, M. Asta, R. O. Ritchie, and E. Ma, Universal structural parameter to quantitatively predict metallic glass properties, Nat. Commun. 7, 13733 (2016).
  51. Z. Fan, J. Ding, Q.-J. Li, and E. Ma, Correlating the properties of amorphous silicon with its flexibility volume, Phys. Rev. B 95, 144211 (2017).
  52. Z. Fan, J. Ding, and E. Ma, Making glassy solids ductile at room temperature by imparting flexibility into their amorphous structure, Mater. Res. Lett. 6, 570 (2018).
  53. N. Tuchinda, M. Wagih, and C. A. Schuh, Interstitial solute segregation at triple junctions: Implications for nanomaterials and a case study of hydrogen in palladium, Phys. Rev. Mater. 9, 056002 (2025).
  54. Z. Zhang and C. Deng, Grain boundary segregation prediction with a dual-solute model, Phys. Rev. Mater. 8, 103605 (2024).
  55. M. Wagih and C. A. Schuh, Spectrum of grain boundary segregation energies in a polycrystal, Acta Mater. 181, 228 (2019).
  56. Y. Q. Cheng, E. Ma, and H. W. Sheng, Atomic level structure in multicomponent bulk metallic glass, Phys. Rev. Lett. 102, 245501 (2009).
  57. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117, 1 (1995).
  58. S. Ioffe and C. Szegedy, Batch normalization: Accelerating deep network training by reducing internal covariate shift, in Proceedings of the 32nd International Conference on Machine Learning, edited by F. Bach, and D. Blei, Proceedings of Machine Learning Research, Vol. 37 (PMLR, Lille, 2015), pp. 448–456.
  59. M. Abadi et al., TensorFlow: A system for large-scale machine learning, in 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI 16) (USENIX Association, Savannah, GA, 2016), pp. 265–283.
  60. A. Sergeev and M. Del Balso, Horovod: Fast and easy distributed deep learning in TensorFlow, arXiv:1802.05799.
  61. Y. Zhang, R. Ashcraft, M. i. Mendelev, C. Z. Wang, and K. F. Kelton, Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni62Nb38 alloy, J. Chem. Phys. 145, 204505 (2016).
  62. Y. Q. Cheng, H. W. Sheng, and E. Ma, Relationship between structure, dynamics, and mechanical properties in metallic glass-forming alloys, Phys. Rev. B 78, 014207 (2008).
  63. M. I. Mendelev, F. Zhang, Z. Ye, Y. Sun, M. C. Nguyen, S. R. Wilson, C. Z. Wang, and K. M. Ho, Development of interatomic potentials appropriate for simulation of devitrification of Al90Sm10 alloy, Modelling Simul. Mater. Sci. Eng. 23, 045013 (2015).
  64. S. R. Wilson and M. I. Mendelev, Anisotropy of the solid–liquid interface properties of the Ni–Zr B33 phase from molecular dynamics simulation, Philos. Mag. 95, 224 (2015).
  65. A. P. Bartók, R. Kondor, and G. Csányi, On representing chemical environments, Phys. Rev. B 87, 184115 (2013).
  66. X. Wang, L. Valdevit, and P. Cao, Neural network for predicting Peierls barrier spectrum and its influence on dislocation motion, Acta Mater. 267, 119696 (2024).
  67. S. Huang, J. Zhang, H. Fu, Y. Xiong, S. Ma, X. Xiang, B. Xu, W. Lu, Y. Zhang, W. J. Weber, S. Zhao, Irradiation performance of high entropy ceramics: A comprehensive comparison with conventional ceramics and high entropy alloys, Prog. Mater Sci. 143, 101250 (2024).
  68. Z. Fang and Q. Yan, Leveraging persistent homology features for accurate defect formation energy predictions via graph neural networks, Chem. Mater. 37, 1531 (2025).
  69. Z. Fan, Structural origin of the anisotropic local mechanical response of amorphous silicon, Phys. Rev. Mater. 8, L060601 (2024).
  70. Z. Fan and H. Tanaka, Microscopic mechanisms of pressure-induced amorphous-amorphous transitions and crystallisation in silicon, Nat. Commun. 15, 368 (2024).
  71. A. P. Bartók, J. Kermode, N. Bernstein, and G. Csányi, Machine learning a general-purpose interatomic potential for silicon, Phys. Rev. X 8, 041048 (2018).
  72. L. Zhang, H. Wang, R. Car, and W. E, Phase diagram of a deep potential water model, Phys. Rev. Lett. 126, 236001 (2021).
  73. Z. Fan, D. Rawat, P. Zarzycki, M. L. Whittaker, and M. Asta, Multistage nucleation pathway in LiF molten salt mirrors the crystal–melt interface structure, Proc. Natl. Acad. Sci. USA 122, e2425702122 (2025).
  74. Z. Fan, M. L. Whittaker, and M. Asta, Efficient machine learning interatomic potentials robust for liquid and multiple solid polymorphs of NaF and KF, Phys. Rev. Mater. 9, 103406 (2025).
  75. Y. Wang, J. Ding, Z. Fan, L. Tian, M. Li, H. Lu, Y. Zhang, E. Ma, J. Li, and Z. Shan, Tension–compression asymmetry in amorphous silicon, Nat. Mater. 20, 1371 (2021).
  76. P. M. Piaggi, J. Weis, A. Z. Panagiotopoulos, P. G. Debenedetti, and R. Car, Homogeneous ice nucleation in an ab initio machine-learning model of water, Proc. Natl. Acad. Sci. USA 119, e2207294119 (2022).
  77. Z. Fan, H. Wang, Y. Wu, X. J. Liu, and Z. P. Lu, Thermoelectric high-entropy alloys with low lattice thermal conductivity, RSC Adv. 6, 52164 (2016).
  78. Z. Fan, H. Wang, Y. Wu, X. Liu, and Z. Lu, Thermoelectric performance of PbSnTeSe high-entropy alloys, Mater. Res. Lett. 5, 187 (2017).
  79. E. P. George, D. Raabe, and R. O. Ritchie, High-entropy alloys, Nat. Rev. Mater. 4, 515 (2019).
  80. C. Oses, C. Toher, and S. Curtarolo, High-entropy ceramics, Nat. Rev. Mater. 5, 295 (2020).
  81. Z. Fan, Figshare (2025), https://doi.org/10.6084/m9.figshare.29642144.

Outline

Information

Phys. Rev. Materials 10, 053803– Published 14 May, 2026
  • Received 25 July 2025
  • Revised 29 December 2025
  • Accepted 28 April 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation