# Targeting the partition function of chemically disordered materials with a generative approach based on inverse variational autoencoders

arXiv: https://arxiv.org/abs/2408.14928 · HTML: https://mlsanity.com/paper/2408.14928/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 27 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Guided Variational Autoencoder for Disentanglement Learning](https://mlsanity.com/paper/2004.01255/) (2020)
- [Categorical Normalizing Flows via Continuous Transformations](https://mlsanity.com/paper/2006.09790/) (2020)
- [An Analysis of State-of-the-art Activation Functions For Supervised Deep Neural Network](https://mlsanity.com/paper/2104.02523/) (2021)
- [Analogical discovery of disordered perovskite oxides by crystal structure information hidden in unsupervised material fingerprints](https://mlsanity.com/paper/2105.11877/) (2021)
- [Approximate sampling and estimation of partition functions using neural networks](https://mlsanity.com/paper/2209.10423/) (2022)

## Built on by (most cited first, 1 of 1)

- [Thermodynamic properties of chemically disordered compounds via AI-driven estimation of partition function with the PULSE method](https://mlsanity.com/paper/2605.28594/) (2026)

## Abstract (arXiv)

Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an excessive amount of configurations or do not ensure that the configuration space has been properly covered. In this work, we propose a novel approach where generative machine learning is used to yield a representative set of configurations for accurate property evaluation and provide accurate estimations of atomic-scale properties with minimal computational cost. Our method employs a specific type of variational autoencoder with inverse roles for the encoder and decoder, enabling the application of an unsupervised active learning scheme that does not require any initial training database. The model iteratively generates configuration batches, whose properties are computed with conventional atomic-scale methods. These results are then fed back into the model to estimate the partition function, repeating the process until convergence. We illustrate our approach by computing point-defect formation energies and concentrations in (U, Pu)O2 mixed-oxide fuels. In addition, the ML model provides valuable insights into the physical factors influencing the target property. Our method is generally applicable to explore other properties, such as atomic-scale diffusion coefficients, in ideally or non-ideally disordered materials like high-entropy alloys.