Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene
Source abstract
Abstract
Abstract We present a way to dramatically accelerate Gaussian process models for interatomic force fields based on many-body kernels by mapping both forces and uncertainties onto functions of low-dimensional features. This allows for automated active learning of models combining near-quantum accuracy, built-in uncertainty, and constant cost of evaluation that is comparable to classical analytical models, capable of simulating millions of atoms. Using this approach, we perform large-scale molecular dynamics simulations of the stability of the stanene monolayer. We discover an unusual phase transformation mechanism of 2D stanene, where ripples lead to nucleation of bilayer defects, densification into a disordered multilayer structure, followed by formation of bulk liquid at high temperature or nucleation and growth of the 3D bcc crystal at low temperature. The presented method opens possibilities for rapid development of fast accurate uncertainty-aware models for simulating long-time large-scale dynamics of complex materials.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Machine Learning in Materials Science · Nanopore and Nanochannel Transport Studies · Block Copolymer Self-Assembly
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (62)
Show source-provided references
1. Van Duin, A. C., Dasgupta, S., Lorant, F. & Goddard, W. A. Reaxff: a reactive force field for hydrocarbons. J. Phys. Chem. A 105, 9396–9409 (2001).10.1021/jp004368u ↗
2. Chenoweth, K., Van Duin, A. C. & Goddard, W. A. Reaxff reactive force field for molecular dynamics simulations of hydrocarbon oxidation. J. Phys. Chem. A 112, 1040–1053 (2008).10.1021/jp709896w ↗
3. Baskes, M. Application of the embedded-atom method to covalent materials: a semiempirical potential for silicon. Phys. Rev. Lett. 59, 2666 (1987).10.1103/PhysRevLett.59.2666 ↗
4. Lindsay, L. & Broido, D. Optimized tersoff and brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene. Phys. Rev. B 81, 205441 (2010).10.1103/PhysRevB.81.205441 ↗
5. 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 ↗
6. Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 134, 074106 (2011).10.1063/1.3553717 ↗
7. Behler, J. Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations. Phys. Chem. Chem. Phys. 13, 17930–17955 (2011).10.1039/c1cp21668f ↗
8. Behler, J. Constructing high-dimensional neural network potentials: a tutorial review. Int. J. Quantum Chem. 115, 1032–1050 (2015).10.1002/qua.24890 ↗
9. Behler, J. Perspective: machine learning potentials for atomistic simulations. J. Chem. Phys. 145, 170901 (2016).10.1063/1.4966192 ↗
10. Mailoa, J. P. et al. A fast neural network approach for direct covariant forces prediction in complex multi-element extended systems. Nat. Mach. Intell. 1, 471–479 (2019).10.1038/s42256-019-0098-0 ↗
11. 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 ↗
12. Batzner, S. et al. Se (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. https://arxiv.org/abs/2101.03164 (2021).10.21203/rs.3.rs-244137/v1 ↗
13. Shapeev, A. V. Moment tensor potentials: a class of systematically improvable interatomic potentials. Multiscale Model. Simul. 14, 1153–1173 (2016).10.1137/15M1054183 ↗
14. Podryabinkin, E. V. & Shapeev, A. V. Active learning of linearly parametrized interatomic potentials. Comput. Mater. Sci. 140, 171–180 (2017).10.1016/j.commatsci.2017.08.031 ↗
15. Hodapp, M. & Shapeev, A. In operando active learning of interatomic interaction during large-scale simulations. Mach. Learn.: Sci. Technol. 1, 045005 (2020).
16. Vandermause, J. et al. On-the-fly active learning of interpretable bayesian force fields for atomistic rare events. npj Comput. Mater. 6, 1–11 (2020).10.1038/s41524-020-0283-z ↗
17. Lim, J. S. et al. Evolution of metastable structures at bimetallic surfaces from microscopy and machine-learning molecular dynamics. J. Am. Chem. Soc. 142, 15907–15916 (2020).10.1021/jacs.0c06401 ↗
18. 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 ↗
19. Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, 184115 (2013).10.1103/PhysRevB.87.184115 ↗
20. Bartók, A. P. & Csányi, G. Gaussian approximation potentials: a brief tutorial introduction. Int. J. Quantum Chem. 115, 1051–1057 (2015).10.1002/qua.24927 ↗
21. Bartók, A. P., Kermode, J., Bernstein, N. & Csányi, G. Machine learning a general-purpose interatomic potential for silicon. Phys. Rev. X 8, 041048 (2018).
22. Thompson, A. P., Swiler, L. P., Trott, C. R., Foiles, S. M. & Tucker, G. J. Snap: automated generation of quantum-accurate interatomic potentials. J. Comput. Phys. 285, 316–330 (2015).10.1016/j.jcp.2014.12.018 ↗
23. Schütt, K. et al. Schnet: a continuous-filter convolutional neural network for modeling quantum interactions. In Proc. Advances in Neural Information Processing Systems, 991–1001 (2017).
24. Schütt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A. & Müller, K.-R. Schnet–a deep learning architecture for molecules and materials. J. Chem. Phys. 148, 241722 (2018).10.1063/1.5019779 ↗
25. Schütt, K. et al. Schnetpack: a deep learning toolbox for atomistic systems. J. Chem. Theory Comput. 15, 448–455 (2018).10.1021/acs.jctc.8b00908 ↗
26. Zhang, L., Han, J., Wang, H., Car, R. & Weinan, E. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120, 143001 (2018).10.1103/PhysRevLett.120.143001 ↗
27. Wang, H., Zhang, L., Han, J. & Weinan, E. Deepmd-kit: a deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 228, 178–184 (2018).10.1016/j.cpc.2018.03.016 ↗
28. Han, J., Zhang, L., Car, R. & E, W. Deep potential: a general representation of a many-body potential energy surface. Commun. Comput. Phys. 23, 629–639 (2018).10.4208/cicp.OA-2017-0213 ↗
29. Musil, F., Willatt, M. J., Langovoy, M. A. & Ceriotti, M. Fast and accurate uncertainty estimation in chemical machine learning. J. Chem. Theory Comput. 15, 906–915 (2019).10.1021/acs.jctc.8b00959 ↗
30. Peterson, A. A., Christensen, R. & Khorshidi, A. Addressing uncertainty in atomistic machine learning. Phys. Chem. Chem. Phys. 19, 10978–10985 (2017).10.1039/C7CP00375G ↗
31. Smith, J. S., Nebgen, B., Lubbers, N., Isayev, O. & Roitberg, A. E. Less is more: sampling chemical space with active learning. J. Chem. Phys. 148, 241733 (2018).10.1063/1.5023802 ↗
32. Jinnouchi, R., Lahnsteiner, J., Karsai, F., Kresse, G. & Bokdam, M. Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on the fly with bayesian inference. Phys. Rev. Lett. 122, 225701 (2019).10.1103/PhysRevLett.122.225701 ↗
33. Jinnouchi, R., Karsai, F. & Kresse, G. On-the-fly machine learning force field generation: application to melting points. Phys. Rev. B 100, 014105 (2019).10.1103/PhysRevB.100.014105 ↗
34. Glielmo, A., Zeni, C. & De Vita, A. Efficient nonparametric n-body force fields from machine learning. Phys. Rev. B 97, 184307 (2018).10.1103/PhysRevB.97.184307 ↗
35. Glielmo, A., Sollich, P. & De Vita, A. Accurate interatomic force fields via machine learning with covariant kernels. Phys. Rev. B 95, 214302 (2017).10.1103/PhysRevB.95.214302 ↗
36. Glielmo, A., Zeni, C., Fekete, Á. & De Vita, A. Building nonparametric n-body force fields using gaussian process regression. in Machine Learning Meets Quantum Physics, 67–98 (Springer, 2020).10.1007/978-3-030-40245-7_5 ↗
37. Chmiela, S., Sauceda, H. E., Müller, K.-R. & Tkatchenko, A. Towards exact molecular dynamics simulations with machine-learned force fields. Nat. Commun. 9, 1–10 (2018).10.1038/s41467-018-06169-2 ↗
38. Zuo, Y. et al. Performance and cost assessment of machine learning interatomic potentials. J. Phys. Chem. A 124, 731–745 (2020).10.1021/acs.jpca.9b08723 ↗
39. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).10.1006/jcph.1995.1039 ↗
40. Tang, P. et al. Stable two-dimensional dumbbell stanene: a quantum spin hall insulator. Phys. Rev. B 90, 121408 (2014).10.1103/PhysRevB.90.121408 ↗
41. Cherukara, M. J. et al. Ab initio-based bond order potential to investigate low thermal conductivity of stanene nanostructures. J. Phys. Chem. Lett. 7, 3752–3759 (2016).10.1021/acs.jpclett.6b01562 ↗
42. Bishop, C. M. Pattern Recognition and Machine Learning (Springer, 2006).
43. Murphy, K. P. Machine Learning: a Probabilistic Perspective (MIT Press, 2012).
44. Zhu, F.-f et al. Epitaxial growth of two-dimensional stanene. Nat. Mater. 14, 1020 (2015).10.1038/nmat4384 ↗
45. Deng, J. et al. Epitaxial growth of ultraflat stanene with topological band inversion. Nat. Mater. 17, 1081 (2018).10.1038/s41563-018-0203-5 ↗
46. Liao, M. et al. Superconductivity in few-layer stanene. Nat. Phys. 14, 344 (2018).10.1038/s41567-017-0031-6 ↗
47. Ganz, E., Ganz, A. B., Yang, L.-M. & Dornfeld, M. The initial stages of melting of graphene between 4000 k and 6000 k. Phys. Chem. Chem. Phys. 19, 3756–3762 (2017).10.1039/C6CP06940A ↗
48. Los, J. H., Zakharchenko, K. V., Katsnelson, M. I. & Fasolino, A. Melting temperature of graphene. Phys. Rev. B 91, 045415 (2015).10.1103/PhysRevB.91.045415 ↗
49. Zakharchenko, K. V., Fasolino, A., Los, J. & Katsnelson, M. Melting of graphene: from two to one dimension. J. Phys. Condens. Matter 23, 202202 (2011).10.1088/0953-8984/23/20/202202 ↗
50. Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Modell. Simul. Mater. Sci. Eng. 18, 015012 (2009).10.1088/0965-0393/18/1/015012 ↗
51. Khaliullin, R. Z., Eshet, H., Kühne, T. D., Behler, J. & Parrinello, M. Nucleation mechanism for the direct graphite-to-diamond phase transition. Nat. Mater. 10, 693–697 (2011).10.1038/nmat3078 ↗
52. Bundy, F. Direct conversion of graphite to diamond in static pressure apparatus. J. Chem. Phys. 38, 631–643 (1963).10.1063/1.1733716 ↗
53. Bundy, F. et al. The pressure-temperature phase and transformation diagram for carbon; updated through 1994. Carbon 34, 141–153 (1996).10.1016/0008-6223(96)00170-4 ↗
54. Irifune, T., Kurio, A., Sakamoto, S., Inoue, T. & Sumiya, H. Correction: ultrahard polycrystalline diamond from graphite. Nature 421, 806–806 (2003).10.1038/421806b ↗
55. Britun, V. F., Kurdyumov, A. V. & Petrusha, I. A. Diffusionless nucleation of lonsdaleite and diamond in hexagonal graphite under static compression. Powder Metall. Met. Ceram. 43, 87–93 (2004).10.1023/B:PMMC.0000028276.63784.8e ↗
56. Ohfuji, H. & Kuroki, K. Origin of unique microstructures in nano-polycrystalline diamond synthesized by direct conversion of graphite at static high pressure. J. Mineral. Petrol. Sci. 104, 307–312 (2009).10.2465/jmps.090622i ↗
57. Pang, W. et al. Epitaxial growth of honeycomb-like stanene on au (111). Appl. Surf. Sci. 146224 (2020).10.1016/j.apsusc.2020.146224 ↗
58. Yuhara, J. et al. Large area planar stanene epitaxially grown on ag (111). 2D Mater. 5, 025002 (2018).10.1088/2053-1583/aa9ea0 ↗
59. Gao, J., Zhang, G. & Zhang, Y.-W. Exploring ag (111) substrate for epitaxially growing monolayer stanene: a first-principles study. Sci. Rep. 6, 1–8 (2016).10.1038/s41598-016-0001-8 ↗
60. Rasmussen, C. E. Gaussian processes in machine learning. in Summer School on Machine Learning, 63–71 (Springer, 2003).10.1007/978-3-540-28650-9_4 ↗
61. Talirz, L. et al. Materials cloud, a platform for open computational science. Sci. Data 7, 1–12 (2020).10.1038/s41597-020-00637-5 ↗
62. Xie, Y., Vandermause, J., Sun, L., Cepellotti, A. & Kozinsky, B. Fast bayesian force fields from active learning: study of inter-dimensional transformation of stanene. Materials Cloud Archive 2020.99 (2020) https://doi.org/10.24435/materialscloud:cs-tf.10.24435/materialscloud:cs-tf ↗