The xtalmet package offers a variety of distance functions for comparing crystal structures. These include both binary and continuous as well as compositional and structural functions. It also enables you to evaluate a set of crystals using uniqueness and novelty metrics derived from these distances.

• Documentation: https://wmd-group.github.io/xtalmet/
• Examples: https://github.com/WMD-group/xtalmet/examples

Note: This package is under active development. Please ensure that the version of the package you are using matches the version of the documentation you are referring to.

A central challenge in materials science is the efficient discovery of functional crystals from the vast chemical space. Recently, the inverse design of crystals using advanced machine learning generative models has emerged as a promising approach due to their ability to rapidly generate numerous candidates. However, while these models have become increasingly sophisticated, their evaluation metrics have remained largely unchanged since the seminal work of Xie et al [1] and Zeni et al [2]. To effectively guide model development, these evaluation metrics must also continue to improve. We aim to refine two primary metrics, uniqueness and novelty, by revising the underlying distance function used to compare crystal structures.

[1] Tian Xie et al. Crystal diffusion variational autoencoder for periodic material generation. International Conference on Learning Representations 2022.

[2] Claudio Zeni et al. A generative model for inorganic materials design. Nature 2025.

The latest stable version can be installed via pip:

pip install xtalmet

Two primary features of xtalmet are the calculation of distances between crystals and the uniqueness/novelty evaluation. For the former usage, suppose you have two crystals xtal_1 and xtal_2 (pymatgen.core.Structure) whose distance you want to measure. You can do so with one line of code:

from xtalmet.distance import d_amd
distance = d_amd(xtal_1, xtal_2)

Here, d_amd is a type of continuous distance based on structural fingerprints. For a complete list of available distances, please refer to the documentation.

For the uniqueness/novelty evaluation, imagine that you want to assess a set of crystals gen_xtals (list[pymatgen.core.Structure]) generated from a model trained on the MP20 dataset. This can be done with just a few lines of code:

from xtalmet.evaluator import Evaluator
evaluator = Evaluator(gen_xtals)
uniqueness = evaluator.uniqueness(distance="d_amd")
novelty = evaluator.novelty(train_xtals="mp20", distance="d_amd")

A more detailed tutorial notebook is provided in the examples directory.

Although we have argued that the progress on evaluation metrics is slower than that on generative models, we are not the sole contributors to this field. Our work builds upon several influential studies. We particularly acknowledge the following contributions:

• Zeni et al. [2]: For their implementation of the S.U.N. (Stability / Uniqueness / Novelty) metric.

• Baird et al. [3]: For their code for uniqueness and novelty, and their framework for creating a Python benchmarking package.

• Widdowson et al. [4, 5]: For their work on a continuous structural distance between crystals.

Other studies, while not directly related, were also inspiring in shaping our approach to measuring distances between crystals.
These include the work of Onwuli et al. [6] on distances between compositional embeddings, as well as Hargreaves et al.'s [7] development of optimal transport-based methods for inorganic compositions.

[3] Baird et al. matbench-genmetrics: A Python library for benchmarking crystal structure generative models using time-based splits of Materials Project structures. Journal of Open Source Software 2024.

[4] Widdowson et al. Resolving the data ambiguity for periodic crystals. Advances in Neural Information Processing Systems 2022.

[5] Widdson et al. Average Minimum Distances of periodic point sets - foundational invariants for mapping periodic crystals. MATCH Communications in Mathematical and in Computer Chemistry 2022.

[6] A. Onwuli et al. Element similarity in high-dimensional materials representations. Digital Discovery 2023.

[7] Hargreaves et al. The earth mover’s distance as a metric for the space of inorganic compositions. Chemistry of Materials 2020.

If you find xtalmet useful in your research, please consider citing:

@misc{negishi2025continuousuniquenessnoveltymetrics,
      title={Continuous Uniqueness and Novelty Metrics for Generative Modeling of Inorganic Crystals}, 
      author={Masahiro Negishi and Hyunsoo Park and Kinga O. Mastej and Aron Walsh},
      year={2025},
      eprint={2510.12405},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2510.12405}, 
}