Fourier Neural Operators for Composition-Driven Crystal Structure Discovery

Abstract

Crystalline materials discovery is essential for energy, electronics, and catalysis, but the vast chemical and structural space makes exhaustive screening infeasible. Existing voxel-based methods are limited by the local receptive fields of three-dimensional convolutional neural networks and the posterior collapse of high-dimensional variational autoencoders. Here, we develop a Fourier Neural Operator (FNO)-based crystal-field solver that maps a prescribed chemical formula and lattice parameters to periodic number-density and electron-density fields. By operating on global Fourier modes, the solver captures long-range correlations in periodic crystal fields beyond conventional local convolutions. Building on this solver, we construct a coupled generation-solving framework in which a conditional variational autoencoder generates diverse candidate lattice parameters in a low-dimensional basis-coefficient space, followed by density-field prediction and atomic reconstruction through peak detection, position optimization, and weight optimization. The reconstructed structures are further screened using voxel-level filtering, machine-learning interatomic-potential relaxation, and first-principle calculations. The framework generates novel structures across 104 chemical formulas with competitive reconstruction accuracy, demonstrating high generative diversity and structural validity. By extending Fourier neural operators to periodic crystal fields and coupling them with composition-conditioned lattice generation, our approach provides a scalable route to crystal structure discovery from prescribed chemical compositions.