A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating previously unidentified materials. Our approach solves this bottleneck by coarse-graining the infinite search space of atomic coordinates into a combinatorially enumerable search space. The key idea is to use Wyckoff representations, coordinate-free sets of symmetry-related positions in a crystal, as the input to a machine learning model. Our model demonstrates exceptionally high precision in finding unknown theoretically stable materials, identifying 1569 materials that lie below the known convex hull of previously calculated materials from just 5675 ab initio calculations. Our approach opens up fundamental advances in computational materials discovery.

The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we present a scheme to resolve powder diffraction data into crystal structures with precise atomic coordinates by screening the space of all possible atomic arrangements, i.e., structural prototypes, including those not previously observed, using a pre-trained machine learning (ML) model. This involves (i) enumerating all possible symmetry-confined ways in which a given composition can be accommodated in a given space group, (ii) ranking the element-assigned prototype representations using energies predicted using and perturbing atoms along the degree of freedom allowed by the Wyckoff positions to match the experimental diffraction data, and (iv) validating the thermodynamic stability of the material using density-functional theory. An advantage of the presented method is that it does not rely on a database of previously observed prototypes and is, therefore capable of finding crystal structures with entirely new symmetric arrangements of atoms. We demonstrate the workflow on unidentified x-ray diffraction spectra from the ICDD database and identify a number of stable structures, where a majority turns out to be derivable from known prototypes. However, at least two are found not to be part of our prior structural data sets.

The advent of machine learning in materials science opens the way for exciting and ambitious simulations of large systems and long time scales with the accuracy of ab initio calculations. Recently, several pretrained universal machine learned interatomic potentials (UPMLIPs) have been published, i.e., potentials distributed with a single set of weights trained to target systems across a very wide range of chemistries and atomic arrangements. These potentials raise the hope of reducing the computational cost and methodological complexity of performing simulations compared to models that require for-purpose training. However, the application of these models needs critical evaluation to assess their usability across material types and properties. In this work, we investigate the application of the following UPMLIPs: MACE, CHGNET, and M3GNET to the context of alloy theory. We calculate the mixing enthalpies and volumes of 21 binary alloy systems and compare the results with DFT calculations to assess the performance of these potentials over different properties and types of materials. We find that the small relative energies necessary to correctly predict mixing energies are generally not reproduced by these methods with sufficient accuracy to describe correct mixing behaviors. However, the performance can be significantly improved by supplementing the training data with relevant training data. The potentials can also be used to partially accelerate these calculations by replacing the ab initio structural relaxation step.

Crystalline materials often exhibit a high level of symmetry. However, most generative models do not account for symmetry, but rather model each atom without any constraints on its position or element. We propose a generative model, Wyckoff Diffusion (WyckoffDiff), which generates symmetry-based descriptions of crystals. This is enabled by considering a crystal structure representation that encodes all symmetry, and we design a novel neural network architecture which enables using this representation inside a discrete generative model framework. In addition to respecting symmetry by construction, the discrete nature of our model enables fast generation. We additionally present a new metric, Fréchet Wrenformer Distance, which captures the symmetry aspects of the materials generated, and we benchmark WyckoffDiff against recently proposed generative models for crystal generation. As a proof-of-concept study, we use WyckoffDiff to find new materials below the convex hull of thermodynamical stability.