Crystal structure representations for machine learning models of formation energies

International Journal of Quantum Chemistry

Volumn 115, Issue 16, 2015, Pages 1094-1101

  Faber, Felix ^a   Lindmaa, Alexander ^b   Von Lilienfeld, O Anatole ^a,c   Armiento, Rickard ^b  

^a UNIVERSITY OF BASEL   (Switzerland)

^b LINKÖPING UNIVERSITY   (Sweden)

^c ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

crystal structure; formation energies; machine learning; periodic systems; representations

Indexed keywords

LEARNING SYSTEMS; MACHINE LEARNING; MOLECULES; TIME VARYING SYSTEMS;

ATOMIZATION ENERGIES; COULOMB MATRIX; FEATURE VECTORS; FORMATION ENERGIES; GENERALIZATION ERROR; MACHINE LEARNING MODELS; ORGANIC MOLECULES; REPRESENTATIONS;

CRYSTAL STRUCTURE;

EID: 84936846648     PISSN: 00207608     EISSN: 1097461X     Source Type: Journal    
DOI: 10.1002/qua.24917     Document Type: Article

References (41)

1. M. Rupp, A. Tkatchenko, K.-R. Müller, O. A. von Lilienfeld, Phys. Rev. Lett. 2012, 108, 058301.
2. K. Hansen, G. Montavon, F. Biegler, S. Fazli, M. Rupp, M. Scheffler, O. A. von Lilienfeld, A. Tkatchenko, K.-R. Müller, J. Chem. Theory Comput. 2013, 9, 3404.
3. O. A. von Lilienfeld, Int. J. Quantum Chem. 2013, 113, 1676.
4. K. T. Schütt, H. Glawe, F. Brockherde, A. Sanna, K. R. Müller, E. K. U. Gross, Phys. Rev. B 2014, 89, 205118.
5. G. Montavon, M. Rupp, V. Gobre, A. Vazquez-Mayagoitia, K. Hansen, A. Tkatchenko, K.-R. Müller, O. A. von Lilienfeld, New J. Phys. 2013, 15, 095003.
6. A. Lopez-Bezanilla, O. A. von Lilienfeld, Phys. Rev. B 2014, 89, 235411.
7. L.-F. Arsenault, A. Lopez-Bezanilla, O. A. von Lilienfeld, A. J. Millis, Phys. Rev. B 2014, 90, 155136.
8. O. A. von Lilienfeld, R. Ramakrishnan, M. Rupp, A. Knoll, Int. J. Quantum Chem. 2015, 115, 1084.
9. A. P. Bartõk, R. Kondor, G. Csányi, Phys. Rev. B 2013, 87, 184115.
10. B. Meredig, A. Agrawal, S. Kirklin, J. E. Saal, J. W. Doak, A. Thompson, K. Zhang, A. Choudhary, C. Wolverton, Phys. Rev. B 2014, 89, 094104.
11. G. Pilania, C. Wang, X. Jiang, S. Rajasekaran, R. Ramprasad, Sci. Rep. 2013, 3, 2810.
12. A. P. Bartõk, M. J. Gillan, F. R. Manby, G. Csányi, Phys. Rev. B 2013, 88, 054104.
13. A. E. Hoerl, R. W. Kennard, Technometrics 1970, 12, 55.
14. V. Vovk, In Empirical Inference;, B. Schölkopf, Z. Luo, V. Vovk, Eds.; Springer: Berlin, Heidelberg, 2013; pp. 105-116.
15. T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed.; Springer: New York, 2011.
16. K. Muller, S. Mika, G. Ratsch, K. Tsuda, B. Scholkopf, IEEE Trans. Neural Netw. 2001, 12, 181.
17. V. N. Vapnik, The Nature of Statistical Learning Theory; Springer-Verlag: New York, 1995.
18. B. Schölkopf, A. J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond; The MIT Press: Cambridge, Mass, 2001.
19. B. Schölkopf, A. Smola, K.-R. Müller, Neural Comput. 1998, 10, 1299.
20. I. T. Jolliffe, Principal Component Analysis; Springer: New York, 2002.
21. P. G. H. Golub, D. C. Reinsch, Numer. Math. 1970, 14, 403.
22. J. E. Moussa, Phys. Rev. Lett. 2012, 109, 059801.
23. M. Rupp, A. Tkatchenko, K.-R. Müller, O. A. von Lilienfeld, Phys. Rev. Lett. 2012, 109, 059802.
24. L. C. Blum, J.-L. Reymond, J. Am. Chem. Soc. 2009, 131, 8732.
25. T. Fink, H. Bruggesser, J.-L. Reymond, Angew. Chem. Int. Ed. 2005, 44, 1504.
26. T. Fink, J.-L. Reymond, J. Chem. Inf. Model. 2007, 47, 342.
27. P. Hohenberg, W. Kohn, Phys. Rev. 1964, 136, B864.
28. W. Kohn, L. J. Sham, Phys. Rev. 1965, 140, A1133.
29. J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865.
30. M. Ernzerhof, J. P. Perdew, K. Burke, Int. J. Quantum Chem. 1997, 64, 285.
31. M. Ernzerhof, G. E. Scuseria, J. Chem. Phys. 1999, 110, 5029.
32. R. Ramakrishnan, P. O. Dral, M. Rupp, O. A. von Lilienfeld, Sci. Data 2014, 1, 140022.
33. P. P. Ewald, Ann. Phys. (Berlin) 1921, 369, 253.
34. A. Y. Toukmaji, J. A. Board, Jr,., Comput. Phys. Commun. 1996, 95, 73.
35. R. M. Martin, Electronic Structure: Basic Theory and Practical Methods; Cambridge University Press: Cambridge, 2008.
36. S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, G. Ceder, Comput. Mater. Sci. 2013, 68, 314.
37. S. van der Walt, S. Colbert, G. Varoquaux, Comput. Sci. Eng. 2011, 13, 22.
38. E. Jones, T. Oliphant, P. Peterson, and others, SciPy: Open source scientific tools for Python; http://www.scipy.org/ (accessed on Jan 23, 2015).
39. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, K. A. Persson, APL Mater. 2013, 1, 011002. https://materialsproject.org/ (accessed on Jan 23, 2015).
40. G. Bergerhoff, R. Hundt, R. Sievers, I. D. Brown, J. Chem. Inf. Comput. Sci. 1983, 23, 66.
41. A. Belsky, M. Hellenbrandt, V. L. Karen, P. Luksch, Acta Crystallogr. Sect. B Struct. Sci. 2002, 58, 364.