# Neural network based order parameter for phase transitions and its applications in high-entropy alloys

arXiv: https://arxiv.org/abs/2109.05598 · HTML: https://mlsanity.com/paper/2109.05598/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 65 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 5 of 5)

- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Anomaly Detection With Conditional Variational Autoencoders](https://mlsanity.com/paper/2010.05531/) (2020)
- [DeepDriveMD: Deep-Learning Driven Adaptive Molecular Simulations for Protein Folding](https://mlsanity.com/paper/1909.07817/) (2019)
- [Robust data-driven approach for predicting the configurational energy of high entropy alloys](https://mlsanity.com/paper/1908.03665/) (2019)

## Built on by (most cited first, 4 of 4)

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators](https://mlsanity.com/paper/2403.13858/) (2024)
- [Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal](https://mlsanity.com/paper/2408.07847/) (2024)
- [Autonomous phase discovery](https://mlsanity.com/paper/2609.33802/) (2026)

## Abstract (arXiv)

Phase transition is one of the most important phenomena in nature and plays a central role in materials design. All phase transitions are characterized by suitable order parameters, including the order-disorder phase transition. However, finding a representative order parameter for complex systems is nontrivial, such as for high-entropy alloys. Given variational autoencoder's (VAE) strength of reducing high dimensional data into few principal components, here we coin a new concept of "VAE order parameter". We propose that the Manhattan distance in the VAE latent space can serve as a generic order parameter for order-disorder phase transitions. The physical properties of the order parameter are quantitatively interpreted and demonstrated by multiple refractory high-entropy alloys. Assisted by it, a generally applicable alloy design concept is proposed by mimicking the nature mixing of elements. Our physically interpretable "VAE order parameter" lays the foundation for the understanding of and alloy design by chemical ordering.