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 dose-limited conditions, particularly at electron doses lower than those typically used for standard AET of beam-robust inorganic nanoparticles, the reduced signal-to-noise ratio forces a trade-off among accuracy, robustness, and throughput. Here, we introduce a physics-aware, two-stage neural network (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 simulated reconstructed volumes, covering diverse noise models, material morphologies, and dose settings. Under reduced-dose conditions relative to conventional AET of beam-robust inorganic nanoparticles, PANN significantly improves performance, reducing the atomic coordinate error and leading to an increase in the atomic recovery rate. The framework’s performance on retrospectively reduced-dose experimental AET data of metallic nanoparticles demonstrates robust post-processing capability within this material class. Together with multi-slice simulation-based demonstrations on selected inorganic crystalline dose-sensitive systems, including halide perovskites, zeolites, and quantum dots, these results suggest a route toward extending PANN to dose-sensitive materials.

The authors' abstract, as published at the source. npj Computational Materials, 2026 · DOI ↗