Atomic-resolution studies are routinely being performed in modern materials-science experiments. Artificial-intelligence tools are promising candidates to leverage this valuable - yet underutilized - data in unprecedented, automatic fashion to discover hidden patterns and eventually novel physics. Here, we introduce ARISE (Nat. Commun. 2021, DOI: 10.1038/s41467-021-26511-5), a crystal-structure-identification method based on Bayesian deep learning. As a major step forward, ARISE is robust to structural noise and can treat more than 100 crystal structures, a number that can be extended on demand. While being trained on ideal structures only, ARISE correctly characterizes strongly perturbed single- and polycrystalline systems, from both synthetic and experimental sources. The probabilistic nature of the Bayesian-deep-learning model yields principled uncertainty estimates, which are found to be correlated with crystalline order of metallic nanoparticles in electron-tomography experiments. Application of unsupervised learning to the internal neural-network representations reveals grain boundaries and (unapparent) structural regions sharing interpretable geometrical properties. This work enables the hitherto hindered analysis of noisy atomic structural data from computations or experiments.