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.