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Determining neighborhood phases in hard-sphere systems using machine learning

  • Regular Article - Computational Methods
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Abstract

A challenging problem in particle-based modeling is one of classifying the many structures which involve very large networks of bonds. Based on capacity to judge if a system is amorphous or solid from radial distribution functions, we set up two machine-learning systems able to identify local structures in mono-component hard-sphere simulations. The machines are constituted of logistic or support-vector regressions applied to linear model, second- and third-degree polynomial hypothesis. We labeled the sphere as solid or amorphous following a bond-order parameter and characterized them with radial structure functions. The features were enough to machine-learning systems predicting the labels with great accuracy.

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Data Availability Statement

All data generated or analysed during this study are included in this published article. [Authors’ comment: The paper provides all information to reproduce the data or figures shown. There are no datasets generated during this current study.]

References

  1. G. Ackland, A. Jones, Applications of local crystal structure measures in experiment and simulation. Phys. Rev. B 73, 054104 (2006)

    Article  ADS  Google Scholar 

  2. J.D. Honeycutt, H.C. Andersen, Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem. 91, 4950–4963 (1987)

    Article  Google Scholar 

  3. C.L. Kelchner, S. Plimpton, J. Hamilton, Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085 (1998)

    Article  ADS  Google Scholar 

  4. H. Tsuzuki, P.S. Branicio, J.P. Rino, Structural characterization of deformed crystals by analysis of common atomic neighborhood. Comput. Phys. Commun. 177, 518–523 (2007)

    Article  ADS  Google Scholar 

  5. A. Malins, S.R. Williams, J. Eggers, C.P. Royall, Identification of structure in condensed matter with the topological cluster classification. J. Chem. Phys. 139, 234506 (2013)

    Article  ADS  Google Scholar 

  6. P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784 (1983)

    Article  ADS  Google Scholar 

  7. P.R. ten Wolde, D. Frenkel, Computer simulation study of gas-liquid nucleation in a Lennard-Jones system. J. Chem. Phys. 109, 9901–9918 (1998)

    Article  ADS  Google Scholar 

  8. E.D. Cubuk, S.S. Schoenholz, J.M. Rieser, B.D. Malone, J. Rottler, D.J. Durian, E. Kaxiras, A.J. Liu, Identifying structural flow defects in disordered solids using machine-learning methods. Phys. Rev. Lett. 114, 108001 (2015)

    Article  ADS  Google Scholar 

  9. S.S. Schoenholz, E.D. Cubuk, D.M. Sussman, E. Kaxiras, A.J. Liu, A structural approach to relaxation in glassy liquids. Nat. Phys. 12, 469–471 (2016)

    Article  Google Scholar 

  10. R. Freitas, E.J. Reed, Uncovering atomistic mechanisms of crystallization using machine learning. arXiv preprint arXiv:1909.05915 (2019)

  11. W.F. Reinhart, A.W. Long, M.P. Howard, A.L. Ferguson, A.Z. Panagiotopoulos, Machine learning for autonomous crystal structure identification. Soft Matter 13, 4733–4745 (2017)

    Article  ADS  Google Scholar 

  12. J. Carrasquilla, R.G. Melko, Machine learning phases of matter. Nat. Phys. 13, 431–434 (2017)

    Article  Google Scholar 

  13. E.P. Van Nieuwenburg, Y.-H. Liu, S.D. Huber, Learning phase transitions by confusion. Nat. Phys. 13, 435–439 (2017)

    Article  Google Scholar 

  14. C. Dietz, T. Kretz, M. Thoma, Machine-learning approach for local classification of crystalline structures in multiphase systems. Phys. Rev. E 96, 011301 (2017)

    Article  ADS  Google Scholar 

  15. K. Swanson, S. Trivedi, J. Lequieu, K. Swanson, R. Kondor, Deep learning for automated classification and characterization of amorphous materials. Soft Matter 16, 435–446 (2020)

    Article  ADS  Google Scholar 

  16. T. Schilling, H.J. Schöpe, M. Oettel, G. Opletal, I. Snook, Precursor-mediated crystallization process in suspensions of hard spheres. Phys. Rev. Lett. 105, 025701 (2010)

    Article  ADS  Google Scholar 

  17. L. Filion, M. Hermes, R. Ni, M. Dijkstra, Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: a comparison of simulation techniques. J. Chem. Phys. 133, 244115 (2010)

    Article  ADS  Google Scholar 

  18. L. Filion, R. Ni, D. Frenkel, M. Dijkstra, Simulation of nucleation in almost hard-sphere colloids: the discrepancy between experiment and simulation persists. J. Chem. Phys. 134, 134901 (2011)

    Article  ADS  Google Scholar 

  19. J. Russo, H. Tanaka, The microscopic pathway to crystallization in supercooled liquids. Sci. Rep. 2, 1–8 (2012)

    Article  Google Scholar 

  20. D. Richard, T. Speck, Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling. J. Chem. Phys. 148, 124110 (2018)

    Article  ADS  Google Scholar 

  21. W. van Megen, H. Schöpe, Entropic identification of the first order freezing transition of a suspension of hard sphere particles. Phys. Rev. Lett. 124, 205701 (2020)

    Article  ADS  Google Scholar 

  22. P.N. Pusey, W. Van Megen, Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320, 340–342 (1986)

    Article  ADS  Google Scholar 

  23. J. Harland, W. Van Megen, Crystallization kinetics of suspensions of hard colloidal spheres. Phys. Rev. E 55, 3054 (1997)

    Article  ADS  Google Scholar 

  24. R. Roth, Fundamental measure theory for hard-sphere mixtures: a review. J. Phys. Condens. Matter 22, 063102 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  25. J. Taffs, S.R. Williams, H. Tanaka, C.P. Royall, Structure and kinetics in the freezing of nearly hard spheres. Soft Matter 9, 297–305 (2013)

    Article  ADS  Google Scholar 

  26. T. Palberg, Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives. J. Phys. Condens. Matter 26, 333101 (2014)

    Article  Google Scholar 

  27. R. Jadrich, B. Lindquist, T. Truskett, Unsupervised machine learning for detection of phase transitions in off-lattice systems. I. Foundations. J. Chem. Phys. 149, 194109 (2018)

    Article  ADS  Google Scholar 

  28. E. Boattini, M. Ram, F. Smallenburg, L. Filion, Neural-network-based order parameters for classification of binary hard-sphere crystal structures. Mol. Phys. 116, 3066–3075 (2018)

    Article  ADS  Google Scholar 

  29. M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (Oxford University Press, 2010)

  30. J. Behler, M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007)

    Article  ADS  Google Scholar 

  31. M.N. Bannerman, R. Sargant, L. Lue, Dynamo: a free \(\backslash \)calo (n) general event-driven molecular dynamics simulator. J. Comput. Chem. 32, 3329–3338 (2011)

    Article  Google Scholar 

  32. D.C. Rapaport, D.C.R. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, 2004)

  33. M. Rintoul, S. Torquato, Hard-sphere statistics along the metastable amorphous branch. Phys. Rev. E 58, 532 (1998)

    Article  ADS  Google Scholar 

  34. L.V. Woodcock, Computation of the free energy for alternative crystal structures of hard spheres. Faraday Discuss. 106, 325–338 (1997)

    Article  ADS  Google Scholar 

  35. J Lee Rodgers, W.A. Nicewander, Thirteen ways to look at the correlation coefficient. Am. Stat. 42, 59–66 (1988)

    Article  Google Scholar 

  36. A. Géron, Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems (O‘Reilly Media, 2019)

  37. S. Auer, D. Frenkel, Numerical simulation of crystal nucleation in colloids. Adv. Comput. Simul. 149–208 (2005)

  38. J. Bokeloh, G. Wilde, R. Rozas, R. Benjamin, J. Horbach, Nucleation barriers for the liquid-to-crystal transition in simple metals: experiment vs. simulation. Eur. Phys. J. Spec. Top. 223, 511–526 (2014)

    Article  Google Scholar 

  39. A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials. Model. Simul. Mater. Sci. Eng. 20, 045021 (2012)

    Article  ADS  Google Scholar 

  40. S. Menon, G. Leines, J. Rogal, pyscal: A python module for structural analysis of atomic environments. J. Open Source Softw. 4, 1824 (2019)

  41. Y. Bengio, A. Courville, P. Vincent, Representation learning: a review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell. 35, 1798–1828 (2013)

  42. V. Laparra, S. Jiménez, D. Tuia, G. Camps-Valls, J. Malo, Principal polynomial analysis. Int. J. Neural Syst. 24, 1440007 (2014)

    Article  Google Scholar 

  43. R. Rojas, Neural Networks: A Systematic Introduction (Springer Science & Business Media, 2013)

  44. M.N. Murty, R. Raghava, Support Vector Machines and Perceptrons: Learning, Optimization, Classification, and Application to Social Networks (Springer, 2016)

  45. S. Raschka, Python Machine Learning (Packt Publishing Ltd, 2015)

  46. D.R. Stockwell, A.T. Peterson, Effects of sample size on accuracy of species distribution models. Ecol. Model. 148, 1–13 (2002)

    Article  Google Scholar 

  47. W.F. Reinhart, A.Z. Panagiotopoulos, Automated crystal characterization with a fast neighborhood graph analysis method. Soft Matter 14, 6083–6089 (2018)

    Article  ADS  Google Scholar 

  48. E. Boattini, M. Dijkstra, L. Filion, Unsupervised learning for local structure detection in colloidal systems. J. Chem. Phys. 151, 154901 (2019)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the CENAPAD-SP (Centro Nacional de Processamento de Alto Desempenho em São Paulo) for providing HPC resources - project UNICAMP/FINEP - MCT.

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Correspondence to P. A. F. P. Moreira.

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Quentino, J.V., Moreira, P.A.F.P. Determining neighborhood phases in hard-sphere systems using machine learning. Eur. Phys. J. B 94, 130 (2021). https://doi.org/10.1140/epjb/s10051-021-00140-9

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  • DOI: https://doi.org/10.1140/epjb/s10051-021-00140-9

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