Open Materials Generation with Stochastic Interpolants

The discovery of new materials is essential for enabling technological advancements. Computational approaches for predicting novel materials must effectively learn the manifold of stable crystal structures within an infinite design space. We introduce Open Materials Generation (OMG), a unifying framework for the generative design and discovery of inorganic crystalline materials. OMG employs stochastic interpolants (SI) to bridge an arbitrary base distribution to the target distribution of inorganic crystals via a broad class of tunable stochastic processes, encompassing both diffusion models and flow matching as special cases. In this work, we adapt the SI framework by integrating an equivariant graph representation of crystal structures and extending it to account for periodic boundary conditions in unit cell representations. Additionally, we couple the SI flow over spatial coordinates and lattice vectors with discrete flow matching for atomic species. We benchmark OMG's performance on two tasks: Crystal Structure Prediction (CSP) for specified compositions, and 'de novo' generation (DNG) aimed at discovering stable, novel, and unique structures. In our ground-up implementation of OMG, we refine and extend both CSP and DNG metrics compared to previous works. OMG establishes a new state-of-the-art in generative modeling for materials discovery, outperforming purely flow-based and diffusion-based implementations. These results underscore the importance of designing flexible deep learning frameworks to accelerate progress in materials science.

A picture of the space of typical learnable tasks

We develop a technique to analyze representations learned by deep networks when they are trained on different tasks using supervised, meta- and contrastive learning. We develop a technique to visualize such representations using an isometric embedding of the space of probabilistic models into a lower-dimensional space, i.e., one that preserves pairwise distances. We discover the following surprising phenomena that shed light upon the structure in the space of learnable tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) fine-tuning a model upon a sub-task does not change the representation much if the model was trained for a large number of epochs; (5) episodic meta-learning algorithms fit similar models eventually as that of supervised learning, even if the two traverse different trajectories during training; (6) contrastive learning methods trained on different datasets learn similar representations. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.