- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Letter
  • Open Access

Active learning and element-embedding approach in neural networks for infinite-layer versus perovskite oxides

Armin Sahinovic and Benjamin Geisler*

  • Department of Physics, Universität Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany

  • *benjamin.geisler@uni-due.de
PDF

Phys. Rev. Research 3, L042022 – Published 10 November, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042022

Abstract

Combining density functional theory simulations and active learning of neural networks, we explore formation energies of oxygen vacancy layers, lattice parameters, and their statistical correlations in infinite-layer versus perovskite oxides across the periodic table, and place the superconducting nickelate and cuprate families in a comprehensive context. We show that neural networks are capable of predicting these observables with high precision, using only 30−50% of the data for training. Element embedding autonomously identifies concepts of chemical similarity between the individual elements that are in line with human knowledge. We demonstrate that active learning efficiently composes the training set by an optimal strategy without a priori knowledge, based on the fundamental concepts of entropy and information, and provides systematic control over the prediction accuracy. This offers key ingredients to considerably accelerate scans of large parameter spaces and exemplifies how artificial intelligence may assist on the quantum scale in finding novel materials with optimized properties.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (75)

  1. 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).
  2. 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).
  3. A. Y.-T. Wang, R. J. Murdock, S. K. Kauwe, A. O. Oliynyk, A. Gurlo, J. Brgoch, K. A. Persson, and T. D. Sparks, Machine learning for materials scientists: An introductory guide toward best practices, Chem. Mat. 32, 4954 (2020).
  4. L. Ward, A. Agrawal, A. Choudhary, and C. Wolverton, A general-purpose machine learning framework for predicting properties of inorganic materials, npj Comput. Mater. 2, 16028 (2016).
  5. F. A. Faber, A. Lindmaa, O. A. von Lilienfeld, and R. Armiento, Machine Learning Energies of 2 Million Elpasolite (ABC2D6) Crystals, Phys. Rev. Lett. 117, 135502 (2016).
  6. L. M. Ghiringhelli, J. Vybiral, S. V. Levchenko, C. Draxl, and M. Scheffler, Big Data of Materials Science: Critical Role of the Descriptor, Phys. Rev. Lett. 114, 105503 (2015).
  7. C. J. Bartel, C. Sutton, B. R. Goldsmith, R. Ouyang, C. B. Musgrave, L. M. Ghiringhelli, and M. Scheffler, New tolerance factor to predict the stability of perovskite oxides and halides, Sci. Adv. 5, eaav0693 (2019).
  8. J. Schmidt, J. Shi, P. Borlido, L. Chen, S. Botti, and M. A. L. Marques, Predicting the thermodynamic stability of solids combining density functional theory and machine learning, Chem. Mat. 29, 5090 (2017).
  9. F. Belviso, V. E. P. Claerbout, A. Comas-Vives, N. S. Dalal, F.-R. Fan, A. Filippetti, V. Fiorentini, L. Foppa, C. Franchini, B. Geisler, L. M. Ghiringhelli, A. Groß, S. Hu, J. Íñiguez, S. K. Kauwe, J. L. Musfeldt, P. Nicolini, R. Pentcheva, T. Polcar, W. Ren et al., Viewpoint: Atomic-scale design protocols toward energy, electronic, catalysis, and sensing applications, Inorg. Chem. 58, 14939 (2019).
  10. A. Lopez-Bezanilla and P. B. Littlewood, Growing field of materials informatics: databases and artificial intelligence, MRS Commun. 10, 1 (2020).
  11. 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).
  12. 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).
  13. D. Jha, K. Choudhary, F. Tavazza, W.-k. Liao, A. Choudhary, C. Campbell, and A. Agrawal, Enhancing materials property prediction by leveraging computational and experimental data using deep transfer learning, Nat. Commun. 10, 5316 (2019).
  14. A. Agrawal and A. Choudhary, Deep materials informatics: Applications of deep learning in materials science, MRS Commun. 9, 779 (2019).
  15. 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).
  16. V. Tshitoyan, J. Dagdelen, L. Weston, A. Dunn, Z. Rong, O. Kononova, K. A. Persson, G. Ceder, and A. Jain, Unsupervised word embeddings capture latent knowledge from materials science literature, Nature (London) 571, 95 (2019).
  17. Q. Zhou, P. Tang, S. Liu, J. Pan, Q. Yan, and S.-C. Zhang, Learning atoms for materials discovery, Proc. Natl. Acad. Sci. USA 115, E6411 (2018).
  18. D. Jha, L. Ward, A. Paul, W.-k. Liao, A. Choudhary, C. Wolverton, and A. Agrawal, ElemNet: Deep learning the chemistry of materials from only elemental composition, Sci. Rep. 8, 17593 (2018).
  19. 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, The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
  20. 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).
  21. S. Curtarolo, W. Setyawan, G. L. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy, M. J. Mehl, H. T. Stokes, D. O. Demchenko, and D. Morgan, AFLOW: An automatic framework for high-throughput materials discovery, Comp. Mat. Sci. 58, 218 (2012).
  22. C. Draxl and M. Scheffler, Nomad: The fair concept for big data-driven materials science, MRS Bull. 43, 676 (2018).
  23. D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature (London) 572, 624 (2019).
  24. Y. Nomura, M. Hirayama, T. Tadano, Y. Yoshimoto, K. Nakamura, and R. Arita, Formation of a two-dimensional single-component correlated electron system and band engineering in the nickelate superconductor NdNiO2, Phys. Rev. B 100, 205138 (2019).
  25. P. Jiang, L. Si, Z. Liao, and Z. Zhong, Electronic structure of rare-earth infinite-layer RNiO2(R=La,Nd), Phys. Rev. B 100, 201106(R) (2019).
  26. H. Sakakibara, H. Usui, K. Suzuki, T. Kotani, H. Aoki, and K. Kuroki, Model Construction and a Possibility of Cupratelike Pairing in a New d9 Nickelate Superconductor (Nd,Sr)NiO2, Phys. Rev. Lett. 125, 077003 (2020).
  27. M. Jiang, M. Berciu, and G. A. Sawatzky, Critical Nature of the Ni Spin State in Doped NdNiO2, Phys. Rev. Lett. 124, 207004 (2020).
  28. A. S. Botana and M. R. Norman, Similarities and differences between LaNiO2 and CaCuO2 and Implications for Superconductivity, Phys. Rev. X 10, 011024 (2020).
  29. M. Osada, B. Y. Wang, B. H. Goodge, K. Lee, H. Yoon, K. Sakuma, D. Li, M. Miura, L. F. Kourkoutis, and H. Y. Hwang, A superconducting praseodymium nickelate with infinite layer structure, Nano Lett. 20, 5735 (2020).
  30. F. Lechermann, Late transition metal oxides with infinite-layer structure: Nickelates versus cuprates, Phys. Rev. B 101, 081110(R) (2020).
  31. X. Wu, D. Di Sante, T. Schwemmer, W. Hanke, H. Y. Hwang, S. Raghu, and R. Thomale, Robust dx2−y2-wave superconductivity of infinite-layer nickelates, Phys. Rev. B 101, 060504(R) (2020).
  32. M. Hirayama, T. Tadano, Y. Nomura, and R. Arita, Materials design of dynamically stable d9 layered nickelates, Phys. Rev. B 101, 075107 (2020).
  33. M. Kitatani, L. Si, O. Janson, R. Arita, Z. Zhong, and K. Held, Nickelate superconductors—a renaissance of the one-band Hubbard model, npj Quantum Mater. 5, 59 (2020).
  34. B. Geisler and R. Pentcheva, Fundamental difference in the electronic reconstruction of infinite-layer versus perovskite neodymium nickelate films on SrTiO3(001), Phys. Rev. B 102, 020502(R) (2020).
  35. D. Li, B. Y. Wang, K. Lee, S. P. Harvey, M. Osada, B. H. Goodge, L. F. Kourkoutis, and H. Y. Hwang, Superconducting Dome in Nd1−xSrxNiO2 Infinite Layer Films, Phys. Rev. Lett. 125, 027001 (2020).
  36. M.-Y. Choi, K.-W. Lee, and W. E. Pickett, Role of 4f states in infinite-layer NdNiO2, Phys. Rev. B 101, 020503(R) (2020).
  37. L. Si, W. Xiao, J. Kaufmann, J. M. Tomczak, Y. Lu, Z. Zhong, and K. Held, Topotactic Hydrogen in Nickelate Superconductors and Akin Infinite-Layer Oxides ABO2, Phys. Rev. Lett. 124, 166402 (2020).
  38. Y. Wang, C.-J. Kang, H. Miao, and G. Kotliar, Hund's metal physics: From SrNiO2 to LaNiO2, Phys. Rev. B 102, 161118(R) (2020).
  39. B. Geisler and R. Pentcheva, Correlated interface electron gas in infinite-layer nickelate versus cuprate films on SrTiO3(001), Phys. Rev. Res. 3, 013261 (2021).
  40. R. A. Ortiz, H. Menke, F. Misják, D. T. Mantadakis, K. Fürsich, E. Schierle, G. Logvenov, U. Kaiser, B. Keimer, P. Hansmann, and E. Benckiser, Superlattice approach to doping infinite-layer nickelates, Phys. Rev. B 104, 165137 (2021).
  41. T. Mikolov, K. Chen, G. Corrado, and J. Dean, Efficient estimation of word representations in vector space (2013), arXiv:1301.3781.
  42. T. Lookman, P. V. Balachandran, D. Xue, and R. Yuan, Active learning in materials science with emphasis on adaptive sampling using uncertainties for targeted design, npj Comput. Mater. 5, 21 (2019).
  43. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  44. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  45. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  46. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
  47. We used an energy cutoff of 520 eV and U=3.32, 3.7, 5.3, 3.9, 4.38, 6.2, 3.25, and 6.2 eV for Co, Cr, Fe, Mn, Mo, Ni, V, and W d states, respectively. We ensured k-point convergence of the total energy within a few meV per unit cell (e.g., 12×12×12 for SrTiO3), adjusting the k-point grid to the respective size of the Brillouin zone. This simultaneously renders accurate lattice parameters. Aspects of magnetism are not considered [24, 28, 30, 34]. Rare-earth 4f electrons were consistently frozen in the core [24, 30, 34, 38, 39, 75].
  48. S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, and G. Ceder, Python materials genomics (pymatgen): A robust, open-source python library for materials analysis, Comp. Mat. Sci. 68, 314 (2013).
  49. A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in mott-hubbard insulators, Phys. Rev. B 52, R5467 (1995).
  50. M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, et al., TensorFlow: Large-scale machine learning on heterogeneous systems (2015), software available from tensorflow.org.
  51. F. Chollet, Keras, https://keras.io (2015).
  52. The well-known overbinding of gas-phase O2 molecules in DFT necessitates a correction of E(O2), which we performed such as to reproduce the experimental O2 binding energy of 5.16 eV [64, 65, 66].
  53. This holds for the cubic paraelectric phase; relative to the tetragonal ferroelectric phase (a=3.84, c=4.77Å [58]), which is 205 meV/formula unit lower in energy, the IL geometry features basal expansion and vertical contraction.
  54. M. Hayward and M. Rosseinsky, Synthesis of the infinite layer Ni(I) phase NdNiO2+x by low temperature reduction of NdNiO3 with sodium hydride, Solid State Sci. 5, 839 (2003).
  55. M. A. Hayward, M. A. Green, M. J. Rosseinsky, and J. Sloan, Sodium hydride as a powerful reducing agent for topotactic oxide deintercalation: Synthesis and characterization of the Nickel(I) oxide LaNiO2, J. Am. Chem. Soc. 121, 8843 (1999).
  56. N. Kobayashi, Z. Hiroi, and M. Takano, Compounds and phase relations in the SrO-CaO-CuO system under high pressure, J. Solid State Chem. 132, 274 (1997).
  57. Z. Zhong, G. Koster, and P. J. Kelly, Prediction of thickness limits of ideal polar ultrathin films, Phys. Rev. B 85, 121411(R) (2012).
  58. Y. Zhang, J. Sun, J. P. Perdew, and X. Wu, Comparative first-principles studies of prototypical ferroelectric materials by LDA, GGA, and SCAN meta-GGA, Phys. Rev. B 96, 035143 (2017).
  59. V. Begum, M. E. Gruner, and R. Pentcheva, Role of the exchange-correlation functional on the structural, electronic, and optical properties of cubic and tetragonal SrTiO3 including many-body effects, Phys. Rev. Mater. 3, 065004 (2019).
  60. J. L. García-Muñoz, J. Rodríguez-Carvajal, P. Lacorre, and J. B. Torrance, Neutron-diffraction study of RNiO3 (R = La, Pr, Nd, Sm): Electronically induced structural changes across the metal-insulator transition, Phys. Rev. B 46, 4414 (1992).
  61. S. J. May, J.-W. Kim, J. M. Rondinelli, E. Karapetrova, N. A. Spaldin, A. Bhattacharya, and P. J. Ryan, Quantifying octahedral rotations in strained perovskite oxide films, Phys. Rev. B 82, 014110 (2010).
  62. M. T. Curnan and J. R. Kitchin, Effects of concentration, crystal structure, magnetism, and electronic structure method on first-principles oxygen vacancy formation energy trends in perovskites, J. Phys. Chem. C 118, 28776 (2014).
  63. C. Mitra, C. Lin, J. Robertson, and A. A. Demkov, Electronic structure of oxygen vacancies in SrTiO3 and LaAlO3, Phys. Rev. B 86, 155105 (2012).
  64. B. Geisler and R. Pentcheva, Inducing n- and p-Type Thermoelectricity in Oxide Superlattices by Strain Tuning of Orbital-Selective Transport Resonances, Phys. Rev. Appl. 11, 044047 (2019).
  65. A. Malashevich and S. Ismail-Beigi, First-principles study of oxygen-deficient LaNiO3 structures, Phys. Rev. B 92, 144102 (2015).
  66. B. Geisler and R. Pentcheva, Competition of defect ordering and site disproportionation in strained LaCoO3 on SrTiO3(001), Phys. Rev. B 101, 165108 (2020).
  67. F. Nestola, N. Korolev, M. Kopylova, N. Rotiroti, D. G. Pearson, M. G. Pamato, M. Alvaro, L. Peruzzo, J. J. Gurney, A. E. Moore, and J. Davidson, CaSiO3 perovskite in diamond indicates the recycling of oceanic crust into the lower mantle, Nature (London) 555, 237 (2018).
  68. In this work, we calculated the data for all materials in advance. If this were not the case, the data would be generated on the fly by DFT exclusively for those materials that are requested by the active-learning algorithm.
  69. S. Kirklin, J. E. Saal, B. Meredig, A. Thompson, J. W. Doak, M. Aykol, S. Rühl, and C. Wolverton, The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies, npj Comput. Mater. 1, 15010 (2015).
  70. L. van der Maaten and G. Hinton, Visualizing data using t-SNE, J. Mach. Learn. Res. 9, 2579 (2008).
  71. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011).
  72. B. Geisler, A. Blanca-Romero, and R. Pentcheva, Design of n- and p-type oxide thermoelectrics in LaNiO3/SrTiO3(001) superlattices exploiting interface polarity, Phys. Rev. B 95, 125301 (2017).
  73. B. Geisler and R. Pentcheva, Confinement- and strain-induced enhancement of thermoelectric properties in LaNiO3/LaAlO3(001) superlattices, Phys. Rev. Mater. 2, 055403 (2018).
  74. G. Xing, J. Sun, Y. Li, X. Fan, W. Zheng, and D. J. Singh, Electronic fitness function for screening semiconductors as thermoelectric materials, Phys. Rev. Mater. 1, 065405 (2017).
  75. J. Liu, M. Kargarian, M. Kareev, B. Gray, P. J. Ryan, A. Cruz, N. Tahir, Y.-D. Chuang, J. Guo, J. M. Rondinelli, J. W. Freeland, G. A. Fiete, and J. Chakhalian, Heterointerface engineered electronic and magnetic phases of NdNiO3 thin films, Nat. Commun. 4, 2714 (2013).

Outline

Information

Phys. Rev. Research 3, L042022– Published 10 November, 2021
  • Received 6 April 2021
  • Revised 1 October 2021
  • Accepted 13 October 2021
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