PRISM: Periodic Representation with multIscale and Similarity graph Modelling for enhanced crystal structure property prediction

TL;DR

PRISM introduces a multigraph neural network for crystal property prediction that explicitly encodes unit-cell periodicity and multiscale interactions through four specialized experts (Cell, Similarity, Atomistic, Multiscale) and a learnable fusion mechanism. By integrating periodic feature encoding with both atomistic and cell-scale representations, PRISM achieves state-of-the-art performance on JARVIS, Materials Project, and MatBench benchmarks, with substantial gains in formation energy, band gaps, and hull energies. The framework demonstrates backbone-agnostic robustness and provides interpretable fusion weights that align with physical intuition, offering a scalable and principled approach to crystal-property modeling. While focused on periodic crystals, the method lays groundwork for extending to molecules and larger-scale lattices with potential coarse-grained or supercell extensions in future work.

Abstract

Crystal structures are characterised by repeating atomic patterns within unit cells across three-dimensional space, posing unique challenges for graph-based representation learning. Current methods often overlook essential periodic boundary conditions and multiscale interactions inherent to crystalline structures. In this paper, we introduce PRISM, a graph neural network framework that explicitly integrates multiscale representations and periodic feature encoding by employing a set of expert modules, each specialised in encoding distinct structural and chemical aspects of periodic systems. Extensive experiments across crystal structure-based benchmarks demonstrate that PRISM improves state-of-the-art predictive accuracy, significantly enhancing crystal property prediction.

Figures (6)

• Figure 1: A Overview of the PRISM architecture. Atomic and superatom embeddings are initialised via dedicated encoders, and each PRISM layer updates them until the final representation that is used to predict the property. B The PRISM layer architecture. Each of the representations are aggregated and fused using four expert modules: Cell (global lattice periodicity), Multiscale (atom-superatom bidirectional interactions), Atomistic (radius graph with periodic boundaries), and Similarity (feature-space graph with periodic boundaries).
• Figure 2: Atomistic expert graph $\mathcal{G}_{\mathrm{atomistic}}$ under periodic boundary conditions. A radius-based neighbourhood with cutoff $r_c$ (green spheres) is built around each reference atom (blue), and edges (red) connect atoms within $r_c$ while accounting for periodic images. A Three reference atoms are highlighted, and a radius graph is created around each of them. The resulting lateral links connect adjacent layers of the material, allowing message passing to propagate across layers and correctly encode the geometry. B In this material, the cutoff does not reach lateral neighbours, so edges form mainly along the vertical direction. Message passing is then propagated only vertically, and the model cannot capture the lateral geometry; stacking additional message-passing layers does not restore the missing lateral pathways.
• Figure 3: Illustration of the feature-space neighbourhood $\mathcal{G}_{\mathrm{feat}}$ under periodic boundary conditions. The neighbourhood is built around the blue reference atom and edges (red) link feature-similar atoms within the shown cell. A Two equivalent unit-cell choices lead to different similarity edges if periodicity is ignored, producing inconsistent graphs across equivalent cells. B Proposed periodic-invariant construction. Candidate neighbours (magenta) are first identified in feature space; for each candidate, we then select the minimal periodic image and add the corresponding edge (red), yielding consistent and invariant graphs. C Corner case in which no feature-similar atoms lie inside the reference unit cell. Similar atoms exist only as periodic replicas, resulting in an unconnected $\mathcal{G}_{\mathrm{feat}}$ graph and a vertically connected $\mathcal{G}_{\mathrm{atomistic}}$, which leads to poor information flow for this structure. Nevertheless, the Cell-Space Expert is able to propagate the information in such structures since the $\mathcal{G}_{\mathrm{cell}}$ graph is connected to the image replicas.
• Figure 4: Cell-Space expert graph construction. The superatom (central orange node) connects to periodic replicas within a large cutoff $R_c$ (green circle), encoding lattice-scale periodicity through edges (red). A–B Two equivalent unit-cell choices produce the same set of replica connections because cell transformations preserve the relative distances and directions between the superatom and its periodic images. The only change comes from global rotations, which can be handled by defining an invariant cell conformer, using equivariant message-passing updates conformer, or applying rotational data augmentation CARTNET.
• Figure 5: Multiscale expert graph $\mathcal{G}_{\mathrm{multiscale}}$. The superatom node (yellow) forms a bipartite graph to all atoms in the unit cell, with edges shown in red. In this expert, message passing is feature-only: no distances, directions, or geometric information are used. A and B show two equivalent unit-cell representations of the same material. Because the connectivity depends only on the set of atomic embeddings and not on their coordinates, both representations yield the same graph and updates, making this expert invariant to unit-cell transformations.