# Crystal structure prediction with machine learning-based element substitution

arXiv: https://arxiv.org/abs/2201.11188 · HTML: https://mlsanity.com/paper/2201.11188/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 43 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 2 of 2)

- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Deep Face Recognition: A Survey](https://mlsanity.com/paper/1804.06655/) (2018)

## Built on by (most cited first, 17 of 17)

- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Deep Reinforcement Learning for Inverse Inorganic Materials Design](https://mlsanity.com/paper/2210.11931/) (2022)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [Crystal Transformer: Self-learning neural language model for Generative and Tinkering Design of Materials](https://mlsanity.com/paper/2204.11953/) (2022)
- [Space Group Conditional Flow Matching](https://mlsanity.com/paper/2509.23822/) (2025)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [Discovery of 2D materials using Transformer Network based Generative Design](https://mlsanity.com/paper/2301.05824/) (2023)
- [Shotgun crystal structure prediction using machine-learned formation energies](https://mlsanity.com/paper/2305.02158/) (2023)
- [Crystal structure prediction using neural network potential and age-fitness Pareto genetic algorithm](https://mlsanity.com/paper/2309.06710/) (2023)
- [Generative Design of inorganic compounds using deep diffusion language models](https://mlsanity.com/paper/2310.00475/) (2023)
- [Materials Transformers Language Models for Generative Materials Design: a benchmark study](https://mlsanity.com/paper/2206.13578/) (2022)
- [Composition based oxidation state prediction of materials using deep learning](https://mlsanity.com/paper/2211.15895/) (2022)
- [C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation](https://mlsanity.com/paper/2601.19076/) (2026)
- [AlphaCrystal-II: Distance matrix based crystal structure prediction using deep learning](https://mlsanity.com/paper/2404.04810/) (2024)
- [NextCrystal: a Symmetry-Driven Generative Framework for Crystal Structure Prediction](https://mlsanity.com/paper/2602.17176/) (2026)
- [Lang2Str: Two-Stage Crystal Structure Generation with LLMs and Continuous Flow Models](https://mlsanity.com/paper/2603.03946/) (2026)
- [Generative Discovery of Magnetic Insulators under Competing Physical Constraints](https://mlsanity.com/paper/2604.21073/) (2026)

## Abstract (arXiv)

The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy surface, which in turn can be evaluated using first-principles calculations. However, performing the iterative gradient descent on the potential energy surface using first-principles calculations is prohibitively expensive for complex systems, such as those with many atoms per unit cell. Here, we present a unique methodology for crystal structure prediction (CSP) that relies on a machine learning algorithm called metric learning. It is shown that a binary classifier, trained on a large number of already identified crystal structures, can determine the isomorphism of crystal structures formed by two given chemical compositions with an accuracy of approximately 96.4%. For a given query composition with an unknown crystal structure, the model is used to automatically select from a crystal structure database a set of template crystals with nearly identical stable structures to which element substitution is to be applied. Apart from the local relaxation calculation of the identified templates, the proposed method does not use ab initio calculations. The potential of this substation-based CSP is demonstrated for a wide variety of crystal systems.