Physics-aware neural networks enable robust and full atomic structure determination via low-dose atomic electron tomography

Abstract

Atomic electron tomography (AET) determines the three-dimensional (3D) coordinates and chemical identities of individual atoms from a series of scanning transmission electron microscopy images taken at different tilt angles. However, under the low dose conditions required to mitigate beam damage, the reduced signal-to-noise ratio forces a trade off among accuracy, robustness, and throughput, which ultimately limits the broader application of AET. Here, we introduce a physics aware, two stage neural networks (PANN) that incorporates physical constraints throughout its workflow to achieve accurate AET under low-dose imaging. First, a global local 3D ResUNet refines the initial reconstruction and corrects geometric distortions in the volume. Second, the local density around each identified atom is encoded using 3D Zernike moments. These feature descriptors, along with the atomic coordinates are then processed by a graph attention Transformer to classify the elemental species. We benchmark the PANN workflow using a dataset of 42,588 reconstructed volumes, covering diverse noise models, materials morphologies, and dose settings. Under low dose conditions, PANN significantly improves performance, reducing the atomic coordinates error and leading to an increase in the atomic recovery rate. The framework's performance on experimental lose dose AET data across nanoparticles of varying morphology and composition demonstrate robust generalization. We anticipate this approach will extend the applicability of AET, particularly in investigating materials sensitive to electron dose or chemical state, including halide perovskites, zeolite, and quantum dot.