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From atomically resolved imaging to generative and causal models


The development of high-resolution imaging methods such as electron and scanning probe microscopy and atomic probe tomography have provided a wealth of information on the atomic structure and functionalities of solids. The availability of this data in turn necessitates the development of approaches to derive quantitative physical information, akin to how the development of scattering techniques provided insights into the atomic-level structure of a vast array of materials in the twentieth century. Here we argue that the endeavour to understand local imaging data requires the adaptation of classical macroscopic definitions. For example, the notion of symmetry can be introduced locally only in a probabilistic sense that must balance our knowledge of the material’s physics and other experimental data points with the imaging data at hand. At the same time, this wealth of local data can enable fundamentally new approaches for the description of solids, based on the construction of statistical and physical models that can ‘generate’ the observed structures. Finally, we note that the availability of observational data opens pathways towards exploring causal mechanisms underpinning solid structure and functionality.

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Fig. 1: General representations of solid systems at different length scales.
Fig. 2: Examples of discovering features from structural data.
Fig. 3: Variational autoencoders.
Fig. 4: Connections between observables and measurements.
Fig. 5: Causal and correlative ML.
Fig. 6: Schematic of the causal learning with a VAE.

Data availability

The data pertinent to this article can be accessed via the corresponding references as cited in the relevant publications.

Code availability

The codes pertinent to this article can be accessed via the corresponding references as cited in the relevant publications.


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The core idea and sections on imaging to models work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. The sections on theoretical descriptors was supported by US DOE, Office of Science, Office of Basic Energy Sciences Data, Artificial Intelligence and Machine Learning at DOE Scientific User Facilities. The causal inference and autoencoders section was supported by the Center for Nanophase Materials Sciences (CNMS), which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory.

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S.V.K. proposed the concept and wrote the initial draft of the opinion. A.G. contributed towards writing the section on the description of solids, structural descriptors, static and dynamic systems and making illustrative figures. R.V. contributed towards writing and editing the manuscript, especially the sections on the generative adversarial models and the parts on symmetry and disorder. M.Z. contributed parts on the variational autoencoders and causal learning.

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Correspondence to Sergei V. Kalinin, Rama Vasudevan or Maxim Ziatdinov.

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Nature Physics thanks Philip Moriarty and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Kalinin, S.V., Ghosh, A., Vasudevan, R. et al. From atomically resolved imaging to generative and causal models. Nat. Phys. 18, 1152–1160 (2022).

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