Machine-learned multi-system surrogate models for materials prediction
Source abstract
Abstract
Abstract Surrogate machine-learning models are transforming computational materials science by predicting properties of materials with the accuracy of ab initio methods at a fraction of the computational cost. We demonstrate surrogate models that simultaneously interpolate energies of different materials on a dataset of 10 binary alloys (AgCu, AlFe, AlMg, AlNi, AlTi, CoNi, CuFe, CuNi, FeV, and NbNi) with 10 different species and all possible fcc, bcc, and hcp structures up to eight atoms in the unit cell, 15,950 structures in total. We find that the deviation of prediction errors when increasing the number of simultaneously modeled alloys is <1 meV/atom. Several state-of-the-art materials representations and learning algorithms were found to qualitatively agree on the prediction errors of formation enthalpy with relative errors of <2.5% for all systems.
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Research context
OpenAlex topics: Machine Learning in Materials Science · X-ray Diffraction in Crystallography · Hydrogen embrittlement and corrosion behaviors in metals
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (49)
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1. Curtarolo, S. et al. AFLOWLIB.ORG: A distributed materials properties repository from high-throughput ab initio calculations. Comput. Mater. Sci. 58, 227–235 (2012).10.1016/j.commatsci.2012.02.002 ↗
2. Saal, J. E. et al. Materials design and discovery with high-throughput density functional theory: the open quantum materials database (OQMD). J. Miner. Met. Mater. Soc. 65, 1501–1509 (2013).10.1007/s11837-013-0755-4 ↗
3. Jain, A. et al. Commentary: The materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).10.1063/1.4812323 ↗
4. C. Draxl and M. Scheffler NOMAD: the FAIR concept for big-data-driven materials science. MRS Bull. 43, 676–682 (2018).10.1557/mrs.2018.208 ↗
5. Curtarolo, S. et al. The high-throughput highway to computational materials design. Nat. Mater. 12, 191–201 (2013).10.1038/nmat3568 ↗
6. Isayev, O. et al. Universal fragment descriptors for predicting properties of inorganic crystals. Nat. Commun. 8, 15679 (2017).10.1038/ncomms15679 ↗
7. Walsh, A. Inorganic materials: the quest for new functionality. Nat. Chem. 7, 274 (2015).10.1038/nchem.2213 ↗
8. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).10.1103/PhysRev.136.B864 ↗
9. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).10.1103/PhysRev.140.A1133 ↗
10. Bartók, A. P., Payne, M. C. & Kondor, R. & Csányi, G. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010).10.1103/PhysRevLett.104.136403 ↗
11. Shapeev, A. V. Moment tensor potentials: a class of systematically improvable interatomic potentials. Multiscale. Model. Simul. 14, 1153–1173 (2016).10.1137/15M1054183 ↗
12. Huo, H. and Rupp, M. Unified representation for machine learning of molecules and materials. arXiv preprint arXiv:1704.06439v3, 13754–13769 (2017).
13. Rupp, M. Machine learning for quantum mechanics in a nutshell. Int. J. Quant. Chem. 115, 1058–1073 (2015).10.1002/qua.24954 ↗
14. Schütt, K. T. et al. How to represent crystal structures for machine learning: Towards fast prediction of electronic properties. Phys. Rev. B 89, 205118 (2014).10.1103/PhysRevB.89.205118 ↗
15. Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, 184115 (2013).10.1103/PhysRevB.87.184115 ↗
16. von Lilienfeld, O. A., Ramakrishnan, R., Rupp, M. & Knoll, A. Fourier series of atomic radial distribution functions: a molecular fingerprint for machine learning models of quantum chemical properties. Int. J. Quant. Chem. 115, 1084–1093 (2015).10.1002/qua.24912 ↗
17. Moussa, J. E. Comment on fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 109, 059801 (2012).10.1103/PhysRevLett.109.059801 ↗
18. Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).10.1103/PhysRevLett.98.146401 ↗
19. Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 134, 074106 (2011).10.1063/1.3553717 ↗
20. Behler, J. Representing potential energy surfaces by high-dimensional neural network potentials. J. Phys. Condens. Matter 26, 183001 (2014).10.1088/0953-8984/26/18/183001 ↗
21. Faber, F., Lindmaa, A., von Lilienfeld, O. A. & Armiento, R. Crystal structure representations for machine learning models of formation energies. Int. J. Quant. Chem. 115, 1094–1101 (2015).10.1002/qua.24917 ↗
22. Rasmussen, C. & Williams, C. Gaussian Processes for Machine Learning. (MIT Press, Cambridge, 2006).
23. Sanchez, J. M., Ducastelle, F. & Gratias, D. Generalized cluster description of multicomponent systems. Phys. Stat. Mech. Appl. 128, 334–350 (1984).10.1016/0378-4371(84)90096-7 ↗
24. De Fontaine, D. in Solid State Physics (eds Ehrenreich, H. & Turnbull, D.) Vol. 47, 33–176 (Elsevier, 1994).10.1016/S0081-1947(08)60639-6 ↗
25. van de Walle, C. G. & Ceder, G. Automating first-principles phase diagram calculations. J. Ph. Equilib. 23, 348–359 (2002).10.1361/105497102770331596 ↗
26. Mueller, T. & Ceder, G. Bayesian approach to cluster expansions. Phys. Rev. B 80, 024103 (2009).10.1103/PhysRevB.80.024103 ↗
27. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).10.1038/nature14539 ↗
28. Schmidhuber, J. Deep learning in neural networks: an overview. Neural Netw. 61, 85–117 (2015).10.1016/j.neunet.2014.09.003 ↗
29. Schütt, K. T. et al. SchNet—a deep learning architecture for molecules and materials. J. Chem. Phys. 148, 241722 (2018).10.1063/1.5019779 ↗
30. Lubbers, N., Smith, J. S. & Barros, K. Hierarchical modeling of molecular energies using a deep neural network. J. Chem. Phys. 148, 241715 (2018).10.1063/1.5011181 ↗
31. Mills, K., Spanner, M. & Tamblyn, I. Deep learning and the Schrödinger equation. Phys. Rev. A 96, 042113 (2017).10.1103/PhysRevA.96.042113 ↗
32. Smith, J. S., Isayev, O. & Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 8, 3192–3203 (2017).10.1039/C6SC05720A ↗
33. Schütt, K. T. et al. Quantum-chemical insights from deep tensor neural networks. Nat. Comm. 8, 13890 (2017).10.1038/ncomms13890 ↗
34. Matlock, M. K., Le Dang, N. & Swamidass, S. J. Learning a local-variable model of aromatic and conjugated systems. ACS Cent. Sci. 4, 52–62 (2018).10.1021/acscentsci.7b00405 ↗
35. Gao, X. & Duan, L.-M. Efficient representation of quantum many-body states with deep neural networks. Nat. Commun. 8, 662 (2017).10.1038/s41467-017-00705-2 ↗
36. Faber, F. A., Christensen, A. S., Huang, B. & von Lilienfeld, O. A. Alchemical and structural distribution based representation for universal quantum machine learning. J. Chem. Phys. 148, 241717 (2018).10.1063/1.5020710 ↗
37. Rupp, M., Tkatchenko, A., Müller, K.-R. & von Lilienfeld, O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 108, 058301 (2012).10.1103/PhysRevLett.108.058301 ↗
38. Willatt, M. J., Musil, F. & Ceriotti, M. Theory and practice of atom-density representations for machine learning. arXiv preprint arXiv:1807.00408 (2018).10.1063/1.5090481 ↗
39. Hart, G. L. W. & Forcade, R. W. Algorithm for generating derivative structures. Phys. Rev. B 77, 224115 (2008).10.1103/PhysRevB.77.224115 ↗
40. Vegard, L. Die Konstitution der Mischkristalle und die Raumfüllung der Atome. Z. Phys. 5, 17–26 (1921).10.1007/BF01349680 ↗
41. Denton, A. R. & Ashcroft, N. W. Vergard’s law. Phys. Rev. A 43, 3161 (1991).10.1103/PhysRevA.43.3161 ↗
42. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).10.1103/PhysRevB.59.1758 ↗
43. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).10.1103/PhysRevB.50.17953 ↗
44. Kresse, G. & Hafner, J. Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements. J. Phys. Condens. Matter 6, 8245–8257 (1994).10.1088/0953-8984/6/40/015 ↗
45. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
46. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).10.1016/0927-0256(96)00008-0 ↗
47. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).10.1103/PhysRevB.54.11169 ↗
48. Wisesa, P., McGill, K. A. & Mueller, T. Efficient generation of generalized Monkhorst-Pack grids through the use of informatics. Phys. Rev. B 93, 155109 (2016).10.1103/PhysRevB.93.155109 ↗
49. Morgan, W. S., Jorgensen, J. J., Hess, B. C. & Hart, G. L. W. Efficiency of generalized regular k-point grids. arXiv preprint arXiv:1804.04741 (2018).