Transport novelty distance: a distributional metric for evaluating material generative models

Abstract Recent advances in generative machine learning have opened new possibilities for the discovery and design of novel materials. However, as these models become more sophisticated, the need for rigorous and meaningful evaluation metrics has grown. Existing evaluation approaches often fail to capture both the quality and novelty of generated structures, limiting our ability to assess true generative performance. In this paper, we introduce the Transport Novelty Distance (TNovD) to judge generative models used for materials discovery jointly by the quality and novelty of the generated materials. Based on ideas from optimal transport theory, TNovD uses a coupling between the features of the training and generated sets, which is used to penalize quality and memorization independently. The two regimes are defined by thresholding the pairwise distances of trained and generated features. The features are generated from crystal structures using a graph neural network that is trained to distinguish between materials, their augmented counterparts, and differently sized supercells using contrastive learning. We evaluate our proposed metric on typical toy experiments relevant for crystal structure prediction, including memorization, noise injection and lattice deformations. Additionally, we validate the TNovD on the MP20 validation set and the WBM substitution dataset, demonstrating that it is capable of detecting both memorized structures and unrealistic material representations that are outside of the training data distribution. We also benchmark the performance of several popular material generative models. While introduced for materials, our TNovD framework is domain-agnostic and can be adapted for other areas, such as images and molecules.