Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Machine-learning-accelerated simulations to enable automatic surface reconstruction

Nature Computational Science volume 3, pages 1034–1044 (2023)Cite this article

Subjects

A preprint version of the article is available at arXiv.

Abstract

Understanding material surfaces and interfaces is vital in applications such as catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can, in principle, predict the structure of material surfaces as a function of thermodynamic variables. However, accurate energy simulations are prohibitive when coupled to the vast phase space that must be statistically sampled. Here we present a bi-faceted computational loop to predict surface phase diagrams of multicomponent materials that accelerates both the energy scoring and statistical sampling methods. Fast, scalable and data-efficient machine learning interatomic potentials are trained on high-throughput density-functional-theory calculations through closed-loop active learning. Markov chain Monte Carlo sampling in the semigrand canonical ensemble is enabled by using virtual surface sites. The predicted surfaces for GaN(0001), Si(111) and SrTiO3(001) are in agreement with past work and indicate that the proposed strategy can model complex material surfaces and discover previously unreported surface terminations.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: AutoSurfRecon framework.
Fig. 2: AL procedure for NFF.
Fig. 3: Obtaining the GaN(0001) contracted-monolayer surface reconstruction using VSSR-MC and a classical potential.
Fig. 4: AL for NFF.
Fig. 5: Analyzing dominant SrTiO3(001) surface terminations observed during VSSR-MC runs at different chemical potentials.
Fig. 6: Comparing DFT and NFF energies of double-layer TiO2 terminations, all with the same composition.

Similar content being viewed by others

Data availability

The trained models, DFT data and Jupyter notebooks used for data analysis are available on Zenodo at https://doi.org/10.5281/zenodo.7758174 (ref. 72). Source data are provided with this paper.

Code availability

The VSSR-MC algorithm reported in this work is available on GitHub at https://github.com/learningmatter-mit/surface-sampling. The version of code used in this work is available on Zenodo at https://doi.org/10.5281/zenodo.10086398 (ref. 73).

References

  1. Shi, R., Waterhouse, G. I. & Zhang, T. Recent progress in photocatalytic CO2 reduction over perovskite oxides. Solar RRL 1, 1700126 (2017).

    Article  Google Scholar 

  2. Sumaria, V., Nguyen, L., Tao, F. F. & Sautet, P. Atomic-scale mechanism of platinum catalyst restructuring under a pressure of reactant gas. J. Am. Chem. Soc. 145, 392–401 (2023).

    Article  Google Scholar 

  3. Fabbri, E. et al. Dynamic surface self-reconstruction is the key of highly active perovskite nano-electrocatalysts for water splitting. Nat. Mater. 16, 925–931 (2017).

    Article  Google Scholar 

  4. Zhang, Z., Wei, Z., Sautet, P. & Alexandrova, A. N. Hydrogen-induced restructuring of a Cu(100) electrode in electroreduction conditions. J. Am. Chem. Soc. 144, 19284–19293 (2022).

    Article  Google Scholar 

  5. Sha, Z., Shen, Z., Cali, E., Kilner, J. A. & Skinner, S. J. Understanding surface chemical processes in perovskite oxide electrodes. J. Mater. Chem. 11, 5645–5659 (2023).

    Article  Google Scholar 

  6. Jung, S.-K. et al. Understanding the degradation mechanisms of LiNi0.5Co0.2Mn0.3O2 cathode material in lithium ion batteries. Adv. Energy Mater. 4, 1300787 (2014).

    Article  Google Scholar 

  7. Han, B. et al. From coating to dopant: how the transition metal composition affects alumina coatings on Ni-rich cathodes. ACS Appl. Mater. Interfaces 9, 41291–41302 (2017).

    Article  Google Scholar 

  8. Xu, C. et al. Bulk fatigue induced by surface reconstruction in layered Ni-rich cathodes for Li-ion batteries. Nat. Mater. 20, 84–92 (2021).

    Article  Google Scholar 

  9. Hirata, A., Saiki, K., Koma, A. & Ando, A. Electronic structure of a SrO-terminated SrTiO3(100) surface. Surf. Sci. 319, 267–271 (1994).

    Article  Google Scholar 

  10. Castell, M. R. Scanning tunneling microscopy of reconstructions on the SrTiO3(001) surface. Surf. Sci. 505, 1–13 (2002).

    Article  Google Scholar 

  11. Erdman, N. et al. The structure and chemistry of the TiO2-rich surface of SrTiO3(001). Nature 419, 55–58 (2002).

    Article  Google Scholar 

  12. Heifets, E., Piskunov, S., Kotomin, E. A., Zhukovskii, Y. F. & Ellis, D. E. Electronic structure and thermodynamic stability of double-layered SrTiO3(001) surfaces: ab initio simulations. Phys. Rev. B 75, 115417 (2007).

    Article  Google Scholar 

  13. Li, H., Jiao, Y., Davey, K. & Qiao, S.-Z. Data-driven machine learning for understanding surface structures of heterogeneous catalysts. Angew. Chem. Int. Ed. 135, e202216383 (2023).

    Article  Google Scholar 

  14. Merte, L. R. et al. Structure of an ultrathin oxide on Pt3Sn(111) solved by machine learning enhanced global optimization. Angew. Chem. Int. Ed. 61, e202204244 (2022).

    Article  Google Scholar 

  15. Foiles, S. M., Baskes, M. I. & Daw, M. S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983–7991 (1986).

    Article  Google Scholar 

  16. Nord, J., Albe, K., Erhart, P. & Nordlund, K. Modelling of compound semiconductors: analytical bond-order potential for gallium, nitrogen and gallium nitride. J. Phys. Condensed Matter 15, 5649 (2003).

    Article  Google Scholar 

  17. Kolpak, A. M., Li, D., Shao, R., Rappe, A. M. & Bonnell, D. A. Evolution of the structure and thermodynamic stability of the BaTiO3(001) surface. Phys. Rev. Lett. 101, 036102 (2008).

    Article  Google Scholar 

  18. Wexler, R. B., Qiu, T. & Rappe, A. M. Automatic prediction of surface phase diagrams using ab initio grand canonical Monte Carlo. J. Phys. Chem. C 123, 2321–2328 (2019).

    Article  Google Scholar 

  19. Zhou, X.-F., Oganov, A. R., Shao, X., Zhu, Q. & Wang, H.-T. Unexpected reconstruction of the α-boron (111) surface. Phys. Rev. Lett. 113, 176101 (2014).

    Article  Google Scholar 

  20. Timmermann, J. et al. IrO2 surface complexions identified through machine learning and surface investigations. Phys. Rev. Lett. 125, 206101 (2020).

    Article  Google Scholar 

  21. Wales, D. J. & Doye, J. P. K. Global optimization by basin-hopping and the lowest energy structures of Lennard–Jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111–5116 (1997).

    Article  Google Scholar 

  22. Panosetti, C., Krautgasser, K., Palagin, D., Reuter, K. & Maurer, R. J. Global materials structure search with chemically motivated coordinates. Nano Lett. 15, 8044–8048 (2015).

    Article  Google Scholar 

  23. Obersteiner, V., Scherbela, M., Hörmann, L., Wegner, D. & Hofmann, O. T. Structure prediction for surface-induced phases of organic monolayers: overcoming the combinatorial bottleneck. Nano Lett. 17, 4453–4460 (2017).

    Article  Google Scholar 

  24. Egger, A. T. et al. Charge transfer into organic thin films: a deeper insight through machine-learning-assisted structure search. Adv. Sci. 7, 2000992 (2020).

    Article  Google Scholar 

  25. Bauer, M. N., Probert, M. I. J. & Panosetti, C. Systematic comparison of genetic algorithm and basin hopping approaches to the global optimization of Si(111) surface reconstructions. J. Phys. Chem. A 126, 3043–3056 (2022).

    Article  Google Scholar 

  26. Wang, Q., Oganov, A. R., Zhu, Q. & Zhou, X.-F. New reconstructions of the (110) surface of rutile TiO2 predicted by an evolutionary method. Phys. Rev. Lett. 113, 266101 (2014).

    Article  Google Scholar 

  27. Schusteritsch, G. & Pickard, C. J. Predicting interface structures: from SrTiO3 to graphene. Phys. Rev. B 90, 035424 (2014).

    Article  Google Scholar 

  28. Meldgaard, S. A., Mortensen, H. L., Jørgensen, M. S. & Hammer, B. Structure prediction of surface reconstructions by deep reinforcement learning. J. Phys. Condensed Matter 32, 404005 (2020).

    Article  Google Scholar 

  29. Hess, F. & Yildiz, B. Polar or not polar? The interplay between reconstruction, Sr enrichment, and reduction at the La0.75Sr0.25MnO3(001) surface. Phys. Rev. Mater. 4, 015801 (2020).

  30. Unke, O. T. et al. Machine learning force fields. Chem. Rev. 121, 10142–10186 (2021).

    Article  Google Scholar 

  31. Axelrod, S. et al. Learning matter: materials design with machine learning and atomistic simulations. Acc. Mater. Res. 3, 343–357 (2022).

    Article  Google Scholar 

  32. Bisbo, M. K. & Hammer, B. Efficient global structure optimization with a machine-learned surrogate model. Phys. Rev. Lett. 124, 086102 (2020).

    Article  Google Scholar 

  33. Bisbo, M. K. & Hammer, B. Global optimization of atomic structure enhanced by machine learning. Phys. Rev. B 105, 245404 (2022).

    Article  Google Scholar 

  34. Timmermann, J. et al. Data-efficient iterative training of Gaussian approximation potentials: application to surface structure determination of rutile IrO2 and RuO2. J. Chem. Phys. 155, 244107 (2021).

    Article  Google Scholar 

  35. Rønne, N. et al. Atomistic structure search using local surrogate model. J. Chem. Phys. 157, 174115 (2022).

    Article  Google Scholar 

  36. Han, Y. et al. Prediction of surface reconstructions using MAGUS. J. Chem. Phys. 158, 174109 (2023).

    Article  Google Scholar 

  37. Xu, J., Xie, W., Han, Y. & Hu, P. Atomistic insights into the oxidation of flat and stepped platinum surfaces using large-scale machine learning potential-based grand-canonical Monte Carlo. ACS Catal. 12, 14812–14824 (2022).

    Article  Google Scholar 

  38. Bernardin, F. E. & Rutledge, G. C. Semi-grand canonical Monte Carlo (SGMC) simulations to interpret experimental data on processed polymer melts and glasses. Macromolecules 40, 4691–4702 (2007).

    Article  Google Scholar 

  39. Damewood, J., Schwalbe-Koda, D. & Gómez-Bombarelli, R. Sampling lattices in semi-grand canonical ensemble with autoregressive machine learning. npj Comput. Mater. 8, 61 (2022).

    Article  Google Scholar 

  40. Carrete, J., Montes-Campos, H., Wanzenböck, R., Heid, E. & Madsen, G. K. H. Deep ensembles vs committees for uncertainty estimation in neural-network force fields: comparison and application to active learning. J. Chem. Phys. 158, 204801 (2023).

    Article  Google Scholar 

  41. Tan, A. R., Urata, S., Goldman, S., Dietschreit, J. C. B. & Gómez-Bombarelli, R. Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles. Preprint at https://arxiv.org/abs/2305.01754 (2023).

  42. Schwalbe-Koda, D., Tan, A. R. & Gómez-Bombarelli, R. Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks. Nat. Commun. 12, 5104 (2021).

    Article  Google Scholar 

  43. Fu, X. et al. Forces are not enough: benchmark and critical evaluation for machine learning force fields with molecular simulations. Transactions on Machine Learning Research https://openreview.net/forum?id=A8pqQipwkt (2023).

  44. Damewood, J. et al. Representations of materials for machine learning. Annu. Rev. Mater. Res. 53, 399–426 (2023).

    Article  Google Scholar 

  45. Stephenson, P. C. L., Radny, M. W. & Smith, P. V. A modified Stillinger–Weber potential for modelling silicon surfaces. Surf. Sci. 366, 177–184 (1996).

    Article  Google Scholar 

  46. Northrup, J. E., Neugebauer, J., Feenstra, R. M. & Smith, A. R. Structure of GaN(0001): the laterally contracted Ga bilayer model. Phys. Rev. B 61, 9932–9935 (2000).

    Article  Google Scholar 

  47. Štich, I., Payne, M. C., King-Smith, R. D., Lin, J.-S. & Clarke, L. J. Ab initio total-energy calculations for extremely large systems: application to the Takayanagi reconstruction of Si(111). Phys. Rev. Lett. 68, 1351–1354 (1992).

    Article  Google Scholar 

  48. Smeu, M., Guo, H., Ji, W. & Wolkow, R. A. Electronic properties of Si(111)-7×7 and related reconstructions: density functional theory calculations. Phys. Rev. B 85, 195315 (2012).

    Article  Google Scholar 

  49. Herger, R. et al. Surface of strontium titanate. Phys. Rev. Lett. 98, 076102 (2007).

    Article  Google Scholar 

  50. Hong, C. et al. Anomalous intense coherent secondary photoemission from a perovskite oxide. Nature 617, 493–498 (2023).

    Article  Google Scholar 

  51. Szot, K. & Speier, W. Surfaces of reduced and oxidized SrTiO3 from atomic force microscopy. Phys. Rev. B 60, 5909–5926 (1999).

    Article  Google Scholar 

  52. Kubo, T. & Nozoye, H. Surface structure of SrTiO3(100). Surf. Sci. 542, 177–191 (2003).

    Article  Google Scholar 

  53. Winter, G. & Gómez-Bombarelli, R. Simulations with machine learning potentials identify the ion conduction mechanism mediating non-Arrhenius behavior in LGPS. J. Phys. Energy 5, 024004 (2023).

    Article  Google Scholar 

  54. Millan, R., Bello-Jurado, E., Moliner, M., Boronat, M. & Gomez-Bombarelli, R. Effect of framework composition and NH3 on the diffusion of Cu+ in Cu-CHA catalysts predicted by machine-learning accelerated molecular dynamics. ACS Cent. Sci. 9, 2044–2056 (2023).

  55. Thompson, A. P. et al. LAMMPS—a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).

    Article  Google Scholar 

  56. Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys. Condensed Matter 29, 273002 (2017).

    Article  Google Scholar 

  57. Boes, J. R., Mamun, O., Winther, K. & Bligaard, T. Graph theory approach to high-throughput surface adsorption structure generation. J. Phys. Chem. A 123, 2281–2285 (2019).

    Article  Google Scholar 

  58. Ong, S. P. et al. Python Materials Genomics (pymatgen): a robust, open-source python library for materials analysis. Comput. Mater. Sci. 68, 314–319 (2013).

    Article  Google Scholar 

  59. Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

    Article  Google Scholar 

  60. Jain, A. et al. The Materials Project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).

    Article  Google Scholar 

  61. Schütt, K., Unke, O. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. In Proc. 38th International Conference on Machine Learning, Proc. Machine Learning Research Vol. 139 (eds Meila, M. & Zhang, T.) 9377–9388 (PMLR, 2021).

  62. Martinez-Cantin, R., Tee, K. & McCourt, M. Practical Bayesian optimization in the presence of outliers. In Proc. Twenty-First International Conference on Artificial Intelligence and Statistics, Proc. Machine Learning Research Vol. 84 (eds Storkey, A. & Perez-Cruz, F.) 1722–1731 (PMLR, 2018).

  63. Ramachandran, P., Zoph, B. & Le, Q. V. Searching for activation functions. Preprint at https://arxiv.org/abs/1710.05941 (2017).

  64. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. In Proc. 3rd International Conference on Learning Representations, ICLR 2015 (eds Bengio, Y. & LeCun, Y.) (2015).

  65. Gasteiger, J., Giri, S., Margraf, J. T. & Günnemann, S. Fast and uncertainty-aware directional message passing for non-equilibrium molecules. Machine Learning for Molecules Workshop, NeurIPS 2020 https://ml4molecules.github.io/papers2020/ML4Molecules_2020_paper_35.pdf (2020).

  66. Reuter, K. & Scheffler, M. Composition, structure, and stability of RuO2(110) as a function of oxygen pressure. Phys. Rev, B 65, 035406 (2001).

    Article  Google Scholar 

  67. Heifets, E., Ho, J. & Merinov, B. Density functional simulation of the BaZrO3(011) surface structure. Phys. Rev. B 75, 155431 (2007).

    Article  Google Scholar 

  68. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  Google Scholar 

  69. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  Google Scholar 

  70. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  Google Scholar 

  71. Tadmor, E. B., Elliott, R. S., Sethna, J. P., Miller, R. E. & Becker, C. A. The potential of atomistic simulations and the knowledgebase of interatomic models. JOM 63, 17 (2011).

    Article  Google Scholar 

  72. Du, X. Data for: Machine-learning-accelerated simulations to enable automatic surface reconstruction. Zenodo https://doi.org/10.5281/zenodo.7758174 (2023).

  73. Du, X. learningmatter-mit/surface-sampling. Zenodo https://doi.org/10.5281/zenodo.10086398 (2023).

Download references

Acknowledgements

We thank G. Winter, J. Peng, N. Frey and M. Liu for helpful discussions. We also appreciate editing by J. Peng and A. Hoffman. X.D. acknowledges support from the National Science Foundation Graduate Research Fellowship under grant no. 2141064. J.K.D. was supported by the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program. We are grateful for computation time allocated on the MIT SuperCloud cluster, the MIT Engaging cluster and the NERSC Perlmutter cluster. This material is based on work supported by the Under Secretary of Defense for Research and Engineering under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Under Secretary of Defense for Research and Engineering. Delivered to the US Government with Unlimited Rights, as defined in DFARS Part 252.227-7013 or 7014 (February 2014). Notwithstanding any copyright notice, US Government rights in this work are defined by DFARS 252.227-7013 or DFARS 252.227-7014 as detailed above. Use of this work other than as specifically authorized by the US Government may violate any copyrights that exist in this work.

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Xiaochen Du

  2. Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Xiaochen Du & James K. Damewood

  3. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    James K. Damewood, Jaclyn R. Lunger, Reisel Millan, Bilge Yildiz & Rafael Gómez-Bombarelli

  4. Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Bilge Yildiz

  5. Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, MA, USA

    Bilge Yildiz

  6. Massachusetts Institute of Technology Lincoln Laboratory, Lexington, MA, USA

    Lin Li

Authors
  1. Xiaochen Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James K. Damewood
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jaclyn R. Lunger
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Reisel Millan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bilge Yildiz
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Lin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Rafael Gómez-Bombarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X.D. implemented the sampling algorithm, performed surface modeling, ran DFT calculations, trained the neural networks and carried out surface stability analysis. J.K.D. assisted with sampling algorithm implementation and provided guidance with surface modeling. J.R.L. provided guidance with surface modeling and ran DFT calculations. R.M. provided guidance with neural network training and active learning. B.Y. provided guidance with the choice of surfaces and surface stability analysis. L.L. supervised the research and contributed to securing funding. R.G.-B. conceived the project, supervised the research and contributed to securing funding. All authors contributed to results discussion and paper writing.

Corresponding author

Correspondence to Rafael Gómez-Bombarelli.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Computational Science thanks Mie Andersen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Top view of additional GaN(0001) MC-sampled structures.

The surface reconstructions are rotated in comparison with the reference structure from ref. 46 but contain the same hexagonal pattern.

Extended Data Fig. 2 Comparing classical potential and DFT energies of Si(111) sampled surface reconstructions.

a–c, Structures shown were obtained from constant-composition (canonical) VSSR-MC sampling using the SRS modified Stillinger-Weber potential45 with 3x3 (a), 5x5 (b) and 7x7 (c) unit cells. The SRS energies were obtained from the depicted structures while the DFT energies came from structures further relaxed at the DFT level. * Further relaxation using DFT resulted in the 3x3 DAS structure.

Extended Data Fig. 3 Correlation plot of force MAE with force s.d. over AL generations.

At each AL generation, an ensemble of just three NFF models was able to estimate force s.d. that correlated strongly with force error. Each individual data point represents a sampled structure. Each blue ‘X’ represents a binned average and a best-fit line is drawn through the binned averages. The binned average is calculated by dividing both the force s.d. and force MAE into equal-sized bins. The average force MAE is then plotted against the median force s.d. for each corresponding bin.

Source data

Extended Data Fig. 4 Force distribution over AL generations.

The majority of high-force structures were added in AL generations 1, 2 and 6, which correspond either to random structures or structures obtained through adversarial attack. The three VSSR-MC AL generations produced structures with low force values mostly around 50 eV Å-1 or less.

Source data

Extended Data Fig. 5 Test performance of the best NFF model.

As described in the main paper, the test data is obtained from VSSR-MC runs using the sixth-generation NFF model.

Source data

Extended Data Fig. 6 Strengths and limitations of VSSR-MC.

a,b, Comparison of limited fixed on-lattice sites (a) and denser algorithmically-generated virtual surface sites that can overlap (b). c, Off-lattice reconstructions can be obtained following VSSR-MC discrete sampling at virtual sites and continuous relaxation of surface atoms and adsorbates. d, Amorphous reconstructions with many local minima, however, will likely be difficult for VSSR-MC to sample.

Extended Data Fig. 7 Side view of virtual sites for surfaces studied in this work.

a–d, Pymatgen (a) and CatKit (b) virtual sites for GaN(0001) against the contracted Ga monolayer reconstruction, two-layer pymatgen sites for Si(111) against the 5x5 DAS reconstruction (c), and pymatgen virtual sites for SrTiO3(001) against the double-layer TiO2 reconstruction (d). The dashed lines are a guide for the eye.

Extended Data Fig. 8 Visualizations in the latent space.

a, Clustering of VSSR-MC structures in the NFF latent space visualized in the first three principal components. In the VSSR-MC with clustering AL method, the surface from each cluster with the highest force s.d. is selected for DFT evaluation. b, PCA of training data and the dominant terminations (term.) in the latent space of the sixth-generation model.

Source data

Supplementary information

Supplementary Information

Supplementary Sections: (1) abbreviations used; and (2) surface stability analysis.

Peer Review File

Supplementary Data 1

Comparison of AutoSurfRecon with existing computational methods for surface reconstruction. AutoSurfRecon automatically samples across many surface compositions and configurations while training an accurate NFF for low-cost energy prediction.

Source data

Source Data Fig. 3

Statistical source data: Typical GaN(0001) VSSR-MC run profile.

Source Data Fig. 4

Statistical source data: (b) force error and predicted force s.d. for the sixth-generation model; (c) latent space embedding PCA of surfaces acquired at each AL generation; (d) force and energy predictions of the model at each AL generation on the final test set.

Source Data Fig. 5

Statistical source data: (b) predicted surface free energies for each dominant termination across Sr and O chemical potentials; (c-e) predicted surface free energies of sampled structures at Sr chemical potentials of −10, −7 and −4 eV and O chemical potential of 0 eV.

Source Data Extended Data Fig. 3

Statistical source data: force error and predicted force s.d. over six AL generations.

Source Data Extended Data Fig. 4

Statistical source data: distribution of force magnitudes over six AL generations.

Source Data Extended Data Fig. 5

Statistical source data: predictions of the sixth-generation AL model on final test data.

Source Data Extended Data Fig. 8

Statistical source data: (a) PCA of test data in the latent space of the sixth-generation model; (b) PCA of the sixth-generation training data and dominant terminations in the latent space of the sixth-generation model.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, X., Damewood, J.K., Lunger, J.R. et al. Machine-learning-accelerated simulations to enable automatic surface reconstruction. Nat Comput Sci 3, 1034–1044 (2023). https://doi.org/10.1038/s43588-023-00571-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s43588-023-00571-7

This article is cited by

Search

Advanced search

Quick links

Nature Briefing AI and Robotics

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: AI and Robotics