Crystal Symmetry and Machine Learning for Systematic Materials Discovery

The work presented in this thesis builds on a symmetry-aware representation of crystal structures called protostructures, based on Wyckoff positions: a coordinate free description of symmetry related atomic sites. This formulation transforms the continuous space of atomic coordinates into a discrete and combinatorially enumerable one. We developed a machine learning model, Wren, which is trained on this representation to provide fast estimates of stability and guide exploration toward promising regions of structural space. A GPU-accelerated workflow using machine-learning-based interatomic potentials and parallelized screening allows for the evaluation of billions of candidate structures within practical timeframes.

Building on this framework, the presented work enumerates 39 billion binary and ternary compounds spanning the chemical space from lithium to bromine, identifying over 88,000 new structural prototypes, and about half a million new crystal structures within a stability limit of 100 meV/atom. The approach is further applied to experimentally unresolved powder diffraction data, where it reconstructs crystal structures consistent with measured patterns, demonstrating the workflow’s ability to uncover physically realizable materials beyond known prototypes.

To explore even broader regions of structural complexity, this work introduces WyckoffDiff, a diffusion-based generative model that produces novel, symmetry-consistent protostructures beyond the training distribution, some predicted to be thermodynamically stable.

Since pretrained interatomic potentials form the foundation of this work, their quality was examined through two complementary studies. The first benchmarks their accuracy in reproducing mixing enthalpies across disordered alloys. The second investigates how these potentials capture the topology of potential energy surfaces by probing energy variations along symmetry-constrained pathways, showing how different machine-learning potentials represent local minima and saddle points, and other artifacts. These two benchmarks provides insight into their reliability for structure prediction, and the resulting findings informed the selection and parametrization of models used throughout our screening framework.

Altogether, the work presented in this thesis demonstrates that the combination of coarse grained screening, ML-based interatomic potentials, and high-performance computing can dramatically accelerate the discovery of previously unseen crystal structures. The framework presented in the thesis expands the boundaries of computational materials discovery and represents a step toward a large-scale, perhaps even comprehensive, mapping of all stable crystal structures permitted by chemistry and symmetry.