Exploring Flow Matching Models for Material Generation

Discovering novel inorganic crystalline materials is a key driver of technological advancement, yet creating realistic and diverse structures remains a significant challenge for generative models. These models must not only learn the complex distribution of atomic arrangements but also the geometric symmetries of 3D space. In this thesis, we present a machine-learning model which is able to generate inorganic crystalline material structures unconditionally, but also with a select set of provided conditions. The core of our approach is a composite architecture that generates the material’s components through three interacting submodules for the lattice, atom types, and fractional coordinates. For each submodule we carefully implemented their respective invariance and equivariance constraints into the architecture. For training, we employ Flow Matching (FM), a generative modeling framework closely related to diffusion and score-matching models. We use FM to learn the continuous parameters of the lattice matrix and the fractional coordinates, the latter is defined on a flat torus manifold to correctly handle periodicity. In parallel, the discrete atomic elements are learned via a Discrete Denoising Diffusion Probabilistic Model (D3PM). Lastly, we validate our model via experiments that show strong overall performance. It achieves a 27% stable, uniqueness and novelty rate (S.U.N) for unconditional generation, meaning that the model can indeed generate new materials.