Reconstructing atomic geometries from concise local representations

Local geometric representations of atomistic structures imbued with symmetry have been instrumental in enabling not only accurate and efficient structure–property prediction, but also serving as a powerful lens for visualizing structural geometry and exploring dataset diversity. In this talk, I will present the inverse problem of recovering real-space geometries from descriptors, which has remained comparatively underexplored.

We will examine how local representations encode structure–property relationships and how these connections can be leveraged to recover atomistic geometries. By systematically comparing concise, smooth representations with tunable geometric resolution (via body order or other hyperparameters), I will identify the key ingredients that enable faithful reconstruction of atomic environments despite open questions about their mathematical completeness and invertibility. These findings emphasize the practical trade-offs between completeness, resolution, and smoothness, and highlight how the interplay between properties, representations, and geometry can guide the design of descriptors for both forward and inverse modeling tasks for machine learning for materials.