Material Property Prediction Using Graphs Based on Generically Complete Isometry Invariants
Tóm tắt
The structure–property hypothesis says that the properties of all materials are determined by an underlying crystal structure. The main obstacle was the ambiguity of conventional crystal representations based on incomplete or discontinuous descriptors that allow false negatives or false positives. This ambiguity was resolved by the ultra-fast pointwise distance distribution, which distinguished all periodic structures in the world’s largest collection of real materials (Cambridge structural database). State-of-the-art results in property prediction were previously achieved by graph neural networks based on various graph representations of periodic crystals, including the Crystal Graph with vertices at all atoms in a crystal unit cell. This work adapts the pointwise distance distribution for a simpler graph whose vertex set is not larger than the asymmetric unit of a crystal structure. The new Distribution Graph reduces mean absolute error by 0.6–12% while having 44–88% of the number of vertices when compared to the Crystal Graph when applied on the Materials Project and Jarvis-DFT datasets using CGCNN and ALIGNN. Methods for hyper-parameters selection for the graph are backed by the theoretical results of the pointwise distance distribution and are then experimentally justified.
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Tài liệu tham khảo
Cohen AJ, Mori-Sánchez P, Yang W (2012) Challenges for density functional theory. Chem Rev 112(1):289–320
Calfa BA, Kitchin JR (2016) Property prediction of crystalline solids from composition and crystal structure. AIChE J 62(8):2605–2613. https://doi.org/10.1002/aic.15251
Ropers J, Mosca MM, Anosova O, Kurlin V, Cooper AI (2022) Fast predictions of lattice energies by continuous isometry invariants of crystal structures. In: International conference on data analytics and management in data intensive domains, pp 178–192
Ye W, Chen C, Wang Z, Chu I-H, Ong SP (2018) Deep neural networks for accurate predictions of crystal stability. Nat Commun 9(1):3800–3800. https://doi.org/10.1038/s41467-018-06322-x
Olsthoorn B, Geilhufe RM, Borysov SS, Balatsky AV (2019) Band gap prediction for large organic crystal structures with machine learning. Adv. Quantum Technol. 2(7–8):1900023. https://doi.org/10.1002/qute.201900023
Scarselli F, Gori M, Tsoi AC, Hagenbuchner M, Monfardini G (2008) The graph neural network model. IEEE Trans Neural Netw 20(1):61–80
Widdowson D, Kurlin V (2022) Resolving the data ambiguity for periodic crystals. Adv Neural Inf Process Syst (NeurIPS) 35:24625–24638
Xie T, Grossman JC (2018) Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys Rev Lett 120:145301. https://doi.org/10.1103/PhysRevLett.120.145301
Court CJ, Yildirim B, Jain A, Cole JM (2020) 3-D inorganic crystal structure generation and property prediction via representation learning. J Chem Inf Model 60(10):4518–4535
Louis S-Y, Zhao Y, Nasiri A, Wang X, Song Y, Liu F, Hu J (2020) Graph convolutional neural networks with global attention for improved materials property prediction. Phys Chem Chem Phys 22(32):18141–18148
Schmidt J, Pettersson L, Verdozzi C, Botti S, Marques MA (2021) Crystal graph attention networks for the prediction of stable materials. Sci Adv 7(49):7948
Sanyal S, Balachandran J, Yadati N, Kumar A, Rajagopalan P, Sanyal S, Talukdar P (2018) MT-CGCNN: integrating crystal graph convolutional neural network with multitask learning for material property prediction. arXiv. https://doi.org/10.48550/ARXIV.1811.05660arXiv:1811.05660
Omee SS, Louis SY, Fu N, Wei L, Dey S, Dong R, Li Q, Hu J (2022) Scalable deeper graph neural networks for high-performance materials property prediction. Patterns 3(5):100491
Das K, Samanta B, Goyal P, Lee S-C, Bhattacharjee S, Ganguly N (2022) CrysXPP: an explainable property predictor for crystalline materials. npj Comput Mater 8(1):43. https://doi.org/10.1038/s41524-022-00716-8
Liu S, Du W, Li Y, Li Z, Zheng Z, Duan C, Ma Z-M, Yaghi OM, Anandkumar A, Borgs C, Chayes JT, Guo H, Tang J (2024) Symmetry-informed geometric representation for molecules, proteins, and crystalline materials. In: Advances in neural information processing systems, vol 36
Choudhary K, DeCost B (2021) Atomistic line graph neural network for improved materials property predictions. npj Comput Mater. https://doi.org/10.1038/s41524-021-00650-1
Yan K, Liu Y, Lin Y, Ji S (2022) Periodic graph transformers for crystal material property prediction. Adv Neural Inf Process Syst 35:15066–15080
Jain A, Ong SP, Hautier G, Chen W, Richards WD, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Ka Persson (2013) The materials project: a materials genome approach to accelerating materials innovation. Appl Phys Lett Mater 1(1):011002. https://doi.org/10.1063/1.4812323
Dunn A, Wang Q, Ganose A, Dopp D, Jain A (2020) Benchmarking materials property prediction methods: the matbench test set and automatminer reference algorithm. npj Comput Mater 6(1):138
Ying C, Cai T, Luo S, Zheng S, Ke G, He D, Shen Y, Liu T-Y (2021) Do transformers really perform badly for graph representation? Adv Neural Inf Process Syst 34:28877–28888
Park CW, Wolverton C (2020) Developing an improved crystal graph convolutional neural network framework for accelerated materials discovery. Phys Rev Mater 4(6):063801
Chen C, Ye W, Zuo Y, Zheng C, Ong SP (2019) Graph networks as a universal machine learning framework for molecules and crystals. Chem Mater 31(9):3564–3572
Cheng J, Zhang C, Dong L (2021) A geometric-information-enhanced crystal graph network for predicting properties of materials. Commun Mater 2(1):1–11
Lawton SL, Jacobson RA (1965) The reduced cell and its crystallographic applications. In: Technical report, Ames Lab., Iowa State Univ. of Science and Tech., US
Pulido A, Chen L, Kaczorowski T, Holden D, Little MA, Chong SY, Slater BJ, McMahon DP, Bonillo B, Stackhouse CJ, Stephenson A, Kane CM, Clowes R, Hasell T, Cooper AI, Day GM (2017) Functional materials discovery using energy–structure–function maps. Nature 543(7647):657–664
Widdowson D, Mosca M, Pulido A, Cooper A, Kurlin V (2022) Average minimum distances of periodic point sets—fundamental invariants for mapping all periodic crystals. MATCH Commun Math Comput Chem 87:529–559
Anosova O, Kurlin V (2021) An isometry classification of periodic point sets. In: Lecture notes in computer science (proceedings of DGMM), vol 12708, pp 229–241
Anosova O, Kurlin V (2022) Recognition of near-duplicate periodic patterns by polynomial-time algorithms for a fixed dimension. arxiv:2205.15298
Hargreaves CJ, Dyer MS, Gaultois MW, Kurlin VA, Rosseinsky MJ (2020) The earth mover’s distance as a metric for the space of inorganic compositions. Chem Mater 32:10610–10620
Elkin Y, Kurlin V (2023) A new near-linear time algorithm for k-nearest neighbor search using a compressed cover tree. In: International conference on machine learn, pp 9267–9311
Harary F, Norman RZ (1960) Some properties of line digraphs. Rendiconti del Circolo Matematico di Palermo 9(2):161–168. https://doi.org/10.1007/BF02854581
Hemminger RL (1972) Line digraphs. In: Alavi Y, Lick DR, White AT (eds) Graph theory and applications. Springer, Berlin, Heidelberg, pp 149–163
Hendrycks D, Gimpel K (2016) Gaussian error linear units (GELUs). arXiv:1606.08415
Shao J, Hu K, Wang C, Xue X, Raj B (2020) Is normalization indispensable for training deep neural network? Adv Neural Inf Process Syst 33:13434–13444
Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. https://doi.org/10.48550/ARXIV.1502.03167arXiv:abs/1502.03167
Lei Ba J, Kiros JR, Hinton GE (2016) Layer normalization. ArXiv e-prints, 1607 https://doi.org/10.48550/arXiv.1607.06450
Case DH, Campbell JE, Bygrave PJ, Day GM (2016) Convergence properties of crystal structure prediction by quasi-random sampling. J Chem Theory Comput 12(2):910–924
Yang J, Hu W, Usvyat D, Matthews D, Schütz M, Chan GK-L (2014) Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy. Science 345(6197):640–643
Bogdanov G, Bustos J, Glebov V, Oskolkov E, Tillotson JP, Timofeeva TV (2020) Molecular and crystal structure, lattice energy and DFT calculations of two 2’-(nitro-benzo-yloxy)aceto-phenone isomers. Acta Crystallogr Sect E Crystallogr Commun 76(pt 6):857–861. https://doi.org/10.1107/S2056989020006295
Emery AA, Wolverton C (2017) High-throughput DFT calculations of formation energy, stability and oxygen vacancy formation energy of ABO3 perovskites. Sci Data 4(1):170153. https://doi.org/10.1038/sdata.2017.153
Perdew JP (1985) Density functional theory and the band gap problem. Int J Quantum Chem 28(S19):497–523
Choudhary K, Garrity KF, Reid AC, DeCost B, Biacchi AJ, Hight Walker AR, Trautt Z, Hattrick-Simpers J, Kusne AG, Centrone A et al (2020) The joint automated repository for various integrated simulations (JARVIS) for data-driven materials design. npj Comput Mater 6(1):173
Willmott CJ, Matsuura K (2005) Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim Res 30(1):79–82. https://doi.org/10.3354/cr030079
Kingma D, Ba L (2015) Adam: a method for stochastic optimization. ArXiv e-prints arXiv:1412.6980
Rubner Y, Tomasi C, Guibas LJ (2000) The earth mover’s distance as a metric for image retrieval. Int J Comput Vis 40(2):99
Arnold H (2006) Transformations of the coordinate system (unit-cell transformations). Wiley, Hoboken
Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M (2021) The density fingerprint of a periodic point set. In: 37th International symposium on computational geometry (SoCG 2021), vol 189
Loshchilov I, Hutter F (2018) Decoupled weight decay regularization. In: International conference on learning representations