Learning atomic representations for data-driven materials design

Learning the latent representations of atomic structures has become central to the application of machine learning (ML) in materials science, as such representations provide a unified framework for connecting atomic structures to material properties. Early physics-inspired descriptors facilitated efficient prediction of selected properties but were limited in flexibility and transferability. Recent advances in graph-based representations and graph neural networks (GNNs) have enabled data-driven feature learning frameworks that capture complex chemical environments, long-range interactions, and symmetry-governed responses directly from atomic structures. In this Perspective, we review recent progress in atomic representation learning for crystalline materials, with an emphasis on GNN architectures for predicting scalar, spectral, and tensorial properties. We discuss emerging challenges and opportunities related to high-fidelity datasets, model interpretability, and the integration of ML predictions with experimentally relevant phenomena, including disorder, dynamics, and finite-temperature effects. Finally, we outline future directions in which representation learning serves as a foundation for inverse materials design, leading to the systematic discovery and optimization of materials with targeted functional properties.