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Experimental discovery of structure–property relationships in ferroelectric materials via active learning

A preprint version of the article is available at arXiv.


Emergent functionalities of structural and topological defects in ferroelectric materials underpin an extremely broad spectrum of applications ranging from domain wall electronics to high dielectric and electromechanical responses. Many of these functionalities have been discovered and quantified via local scanning probe microscopy methods. However, the search has until now been based on either trial and error, or using auxiliary information such as the topography or domain wall structure to identify potential objects of interest on the basis of the intuition of operator or pre-existing hypotheses, with subsequent manual exploration. Here we report the development and implementation of a machine learning framework that actively discovers relationships between local domain structure and polarization-switching characteristics in ferroelectric materials encoded in the hysteresis loop. The hysteresis loops and their scalar descriptors such as nucleation bias, coercive bias and the hysteresis loop area (or more complex functionals of hysteresis loop shape) and corresponding uncertainties are used to guide the discovery of these relationships via automated piezoresponse force microscopy and spectroscopy experiments. As such, this approach combines the power of machine learning methods to learn the correlative relationships between high-dimensional data, as well as human-based physics insights encoded into the acquisition function. For ferroelectric materials, this automated workflow demonstrates that the discovery path and sampling points of on- and off-field hysteresis loops are largely different, indicating that on- and off-field hysteresis loops are dominated by different mechanisms. The proposed approach is universal and can be applied to a broad range of modern imaging and spectroscopy methods ranging from other scanning probe microscopy modalities to electron microscopy and chemical imaging.

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Fig. 1: PFM results from PTO film.
Fig. 2: Schematic illustration of active learning with DKL.
Fig. 3: DKL on the pre-acquired dataset for 15% of measured locations.
Fig. 4: DKL reconstruction from randomly sampled data.
Fig. 5: Physics-based descriptors for DKL-BO.
Fig. 6: DKL-BO-based automated PFM experiment.

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The data that support the findings of this study are available at (

Code availability

The code of this study is available at (


  1. Gerber, C. & Lang, H. P. How the doors to the nanoworld were opened. Nat. Nanotechnol. 1, 3–5 (2006).

    Article  Google Scholar 

  2. Oxley, M. P., Lupini, A. R. & Pennycook, S. J. Ultra-high resolution electron microscopy. Rep. Prog. Phys. 80, 64 (2017).

    Article  Google Scholar 

  3. Müller, D. J. et al. Atomic force microscopy-based force spectroscopy and multiparametric imaging of biomolecular and cellular systems. Chem. Rev. 121, 11701–11725 (2020).

  4. Fukuma, T. & Garcia, R. Atomic-and molecular-resolution mapping of solid–liquid interfaces by 3D atomic force microscopy. ACS Nano 12, 11785–11797 (2018).

    Article  Google Scholar 

  5. Gross, L. et al. Atomic force microscopy for molecular structure elucidation. Angew. Chem. Int. Ed. 57, 3888–3908 (2018).

    Article  Google Scholar 

  6. Asenjo, A., Gomezrodriguez, J. M. & Baro, A. M. Current imaging tunneling spectroscopy of metallic deposits on silicon. Ultramicroscopy 42, 933–939 (1992).

    Article  Google Scholar 

  7. Pan, S. H. et al. Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+δ. Nature 403, 746–750 (2000).

    Article  Google Scholar 

  8. Roushan, P. et al. Topological surface states protected from backscattering by chiral spin texture. Nature 460, 1106–1109 (2009).

    Article  Google Scholar 

  9. Pennycook, S. J., Varela, M., Lupini, A. R., Oxley, M. P. & Chisholm, M. F. Atomic-resolution spectroscopic imaging: past, present and future. J. Electron Microsc. 58, 87–97 (2009).

    Article  Google Scholar 

  10. Varela, M. et al. Spectroscopic imaging of single atoms within a bulk solid. Phys. Rev. Lett. 92, 095502 (2004).

    Article  Google Scholar 

  11. Botton, G. A. A new approach to study bonding anisotropy with EELS. J. Electron. Spectrosc. Relat. Phenom. 143, 129–137 (2005).

    Article  Google Scholar 

  12. Noy, A., Frisbie, C. D., Rozsnyai, L. F., Wrighton, M. S. & Lieber, C. M. Chemical force microscopy—exploiting chemically-modified tips to quantify adhesion, friction, and functional-group distributions in molecular assemblies. J. Am. Chem. Soc. 117, 7943–7951 (1995).

    Article  Google Scholar 

  13. Garcia, R. & Perez, R. Dynamic atomic force microscopy methods. Surf. Sci. Rep. 47, 197–301 (2002).

    Article  Google Scholar 

  14. Butt, H. J., Cappella, B. & Kappl, M. Force measurements with the atomic force microscope: technique, interpretation and applications. Surf. Sci. Rep. 59, 1–152 (2005).

    Article  Google Scholar 

  15. Bdikin, I. K., Shvartsman, V. V. & Kholkin, A. L. Nanoscale domains and local piezoelectric hysteresis in Pb(Zn1/3Nb2/3)O3–4.5%PbTIO3 single crystals. Appl. Phys. Lett. 83, 4232–4234 (2003).

    Article  Google Scholar 

  16. Eng, L. M. et al. in Advances in Solid State Physics Vol. 41 (ed. B. Kramer) 287–298 (Springer, 2001).

  17. Kalinin, S. V. et al. Defect-mediated polarization switching in ferroelectrics and related materials: from mesoscopic mechanisms to atomistic control. Adv. Mater. 22, 314–322 (2010).

    Article  Google Scholar 

  18. Jesse, S., Lee, H. N. & Kalinin, S. V. Quantitative mapping of switching behavior in piezoresponse force microscopy. Rev. Sci. Instrum. 77, 073702 (2006).

    Article  Google Scholar 

  19. Jesse, S., Baddorf, A. P. & Kalinin, S. V. Switching spectroscopy piezoresponse force microscopy of ferroelectric materials. Appl. Phys. Lett. 88, 062908 (2006).

    Article  Google Scholar 

  20. Bosman, M., Watanabe, M., Alexander, D. T. L. & Keast, V. J. Mapping chemical and bonding information using multivariate analysis of electron energy-loss spectrum images. Ultramicroscopy 106, 1024–1032 (2006).

    Article  Google Scholar 

  21. Jesse, S. & Kalinin, S. V. Principal component and spatial correlation analysis of spectroscopic-imaging data in scanning probe microscopy. Nanotechnology 20, 085714 (2009).

    Article  Google Scholar 

  22. Wei, Q., Bioucas-Dias, J., Dobigeon, N. & Tourneret, J. Y. Hyperspectral and multispectral image fusion based on a sparse representation. IEEE Trans. Geosci. Remote Sens. 53, 3658–3668 (2015).

    Article  Google Scholar 

  23. Kelley, K. P. et al. Fast scanning probe microscopy via machine learning: non-rectangular scans with compressed sensing and Gaussian process optimization. Small 16, 2002878 (2020).

  24. Kalinin, S. V., Kelley, K., Vasudevan, R. K. & Ziatdinov, M. Toward decoding the relationship between domain structure and functionality in ferroelectrics via hidden latent variables. ACS Appl. Mater. Interfaces 13, 1693–1703 (2021).

    Article  Google Scholar 

  25. Deng, J. et al. ImageNet: a large-scale hierarchical image database. In 2009 IEEE Conference on Computer Vision and Pattern Recognition 248–255 (IEEE, 2009).

  26. Krull, A., Hirsch, P., Rother, C., Schiffrin, A. & Krull, C. Artificial-intelligence-driven scanning probe microscopy. Commun. Phys. 3, 8 (2020).

    Article  Google Scholar 

  27. Dyck, O., Jesse, S. & Kalinin, S. V. A self-driving microscope and the Atomic Forge. MRS Bull. 44, 669–670 (2019).

    Article  Google Scholar 

  28. Kelley, K. P. et al. Dynamic manipulation in piezoresponse force microscopy: creating nonequilibrium phases with large electromechanical response. ACS Nano 14, 10569–10577 (2020).

    Article  Google Scholar 

  29. Requicha, A. et al. in Proc. 2001 1st IEEE Conference on Nanotechnology 81–86 (IEEE, 2001).

  30. Baur, C. et al. Nanoparticle manipulation by mechanical pushing: underlying phenomena and real-time monitoring. Nanotechnology 9, 360 (1998).

    Article  Google Scholar 

  31. Mokaberi, B., Yun, J., Wang, M. & Requicha, A. A. Automated nanomanipulation with atomic force microscopes. In Proc. 2007 IEEE International Conference on Robotics and Automation 1406–1412 (IEEE, 2007).

  32. Xie, H., Onal, C., Régnier, S. & Sitti, M. in Atomic Force Microscopy Based Nanorobotics 237–311 (Springer, 2011).

  33. Mokaberi, B. & Requicha, A. A. Drift compensation for automatic nanomanipulation with scanning probe microscopes. IEEE Trans. Autom. Sci. Eng. 3, 199–207 (2006).

    Article  Google Scholar 

  34. Ovchinnikov, O. S., Jesse, S. & Kalinin, S. V. Adaptive probe trajectory scanning probe microscopy for multiresolution measurements of interface geometry. Nanotechnology 20, 255701 (2009).

  35. Huang, B., Li, Z. & Li, J. An artificial intelligence atomic force microscope enabled by machine learning. Nanoscale 10, 21320–21326 (2018).

    Article  Google Scholar 

  36. Sotres, J., Boyd, H. & Gonzalez-Martinez, J. F. Enabling autonomous scanning probe microscopy imaging of single molecules with deep learning. Nanoscale 13, 9193–9203 (2021).

  37. Kalinin, S. V. et al. Automated and autonomous experiment in electron and scanning probe microscopy. ACS Nano 8, 12604–12627 (2021).

  38. Vasudevan, R. K. et al. Autonomous experiments in scanning probe microscopy and spectroscopy: choosing where to explore polarization dynamics in ferroelectrics. ACS Nano 15, 11253–11262 (2021).

    Article  Google Scholar 

  39. Morioka, H. et al. Suppressed polar distortion with enhanced Curie temperature in in-plane 90-domain structure of a-axis oriented PbTiO3 Film. Appl. Phys. Lett. 106, 042905 (2015).

    Article  Google Scholar 

  40. Jesse, S., Maksymovych, P. & Kalinin, S. V. Rapid multidimensional data acquisition in scanning probe microscopy applied to local polarization dynamics and voltage dependent contact mechanics. Appl. Phys. Lett. 93, 112903 (2008).

    Article  Google Scholar 

  41. Liu, Y., Proksch, R., Wong, C. Y., Ziatdinov, M. & Kalinin, S. V. Disentangling ferroelectric wall dynamics and identification of pinning mechanisms via deep learning. Adv. Mater. 33, 2103680 (2021).

  42. Kalinin, S. V., Steffes, J. J., Liu, Y., Huey, B. D. & Ziatdinov, M. Disentangling ferroelectric domain wall geometries and pathways in dynamic piezoresponse force microscopy via unsupervised machine learning. Nanotechnology 33, 055707 (2021).

    Article  Google Scholar 

  43. Roccapriore, K. M., Ziatdinov, M., Cho, S. H., Hachtel, J. A. & Kalinin, S. V. Predictability of localized plasmonic responses in nanoparticle assemblies. Small 17, 2100181 (2021).

    Article  Google Scholar 

  44. Pearl, J. The seven tools of causal inference, with reflections on machine learning. Commun. ACM 62, 54–60 (2019).

    Article  Google Scholar 

  45. Pearl, J. A linear ‘microscope’ for interventions and counterfactuals. J. Causal Inference 5, 15 (2017).

    MathSciNet  Google Scholar 

  46. Mooij, J. M., Peters, J., Janzing, D., Zscheischler, J. & Scholkopf, B. Distinguishing cause from effect using observational data: methods and benchmarks. J. Mach. Learn. Res. 17, 102 (2016).

    MathSciNet  MATH  Google Scholar 

  47. Choudhury, S. et al. Effect of ferroelastic twin walls on local polarization switching: phase-field modeling. Appl. Phys. Lett. 93, 162901 (2008).

  48. Kalinin, S. V. et al. Intrinsic single-domain switching in ferroelectric materials on a nearly ideal surface. Proc. Natl Acad. Sci. USA 104, 20204–20209 (2007).

    Article  Google Scholar 

  49. Rodriguez, B. J. et al. Unraveling deterministic mesoscopic polarization switching mechanisms: spatially resolved studies of a tilt grain boundary in bismuth ferrite. Adv. Funct. Mater. 19, 2053–2063 (2009).

    Article  Google Scholar 

  50. Rasmussen, C. E. & Williams, C. K. I. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (MIT Press, 2005).

  51. Ziatdinov, M. et al. Imaging mechanism for hyperspectral scanning probe microscopy via Gaussian process modelling. npj Comput. Mater. 6, 21 (2020).

    Article  Google Scholar 

  52. Ziatdinov, M. et al. Predictability as a probe of manifest and latent physics: the case of atomic scale structural, chemical, and polarization behaviors in multiferroic Sm-doped BiFeO3. Appl. Phys. Rev. 8, 011403 (2021).

    Article  Google Scholar 

  53. Shahriari, B., Swersky, K., Wang, Z., Adams, R. P. & Freitas, N. D. Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104, 148–175 (2016).

    Article  Google Scholar 

  54. Wilson, A. G., Hu, Z., Salakhutdinov, R. & Xing, E. P. Deep kernel learning. In Proc. 19th International Conference on Artificial Intelligence and Statistics 370–378 (PMLR, 2016).

  55. Blei, D. M., Kucukelbir, A. & McAuliffe, J. D. Variational inference: a review for statisticians. J. Am. Stat. Assoc. 112, 859–877 (2017).

    Article  MathSciNet  Google Scholar 

  56. Jesse, S. et al. Direct imaging of the spatial and energy distribution of nucleation centres in ferroelectric materials. Nat. Mater. 7, 209–215 (2008).

    Article  Google Scholar 

  57. Aravind, V. R. et al. Correlated polarization switching in the proximity of a 180 degrees domain wall. Phys. Rev. B 82, 024111 (2010).

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The development of the machine learning workflows was supported by the Oak Ridge National Laboratory’s Center for Nanophase Materials Sciences (CNMS), a US Department of Energy, Office of Science User Facility (M.A.Z., R.K.V.). The deployment of the machine learning workflows on the operational microscope was supported as part of the center for 3D Ferroelectric Microelectronics (3DFeM), an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences under award no. DE-SC0021118 (Y.L., K.P.K., S.V.K.).

Author information

Authors and Affiliations



S.V.K. conceived the project and M.A.Z. realized the DKL-BO workflow. Y.L. performed detailed analyses with basic workflow from M.A.Z. Y.L. deployed the DKL to PFM measurement and obtained results. R.K.V. and K.P.K. helped with the deployment. H.F. provided the PTO sample. All authors contributed to discussions and the final manuscript.

Corresponding authors

Correspondence to Maxim A. Ziatdinov or Sergei V. Kalinin.

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The authors declare no competing interests.

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Nature Machine Intelligence thanks Adam Foster and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Video 1

DKL reconstruction of coercive field based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of coercive field.

Supplementary Video 2

DKL reconstruction of off-field loop area based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of off-field loop area.

Supplementary Video 3

DKL reconstruction of off-field loop width based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of off-field loop width.

Supplementary Video 4

DKL reconstruction of positive coercive field based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of positive coercive field.

Supplementary Video 5

DKL reconstruction of negative coercive field based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of negative coercive field.

Supplementary Video 6

DKL-BO experiment process of off-field loop area discovery shown as a video of the acquisition function values and label of next measurement, the black cross in the video indicates the next measurement point. The acquisition function is guided by off-field loop area.

Supplementary Video 7

DKL-BO experiment process of on-field loop area discovery shown as a video of the acquisition function values and label of next measurement, the black cross in the video indicates the next measurement point. The acquisition function is guided by on-field loop area.

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Liu, Y., Kelley, K.P., Vasudevan, R.K. et al. Experimental discovery of structure–property relationships in ferroelectric materials via active learning. Nat Mach Intell 4, 341–350 (2022).

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