# Estimating Gibbs free energies via isobaric-isothermal flows

arXiv: https://arxiv.org/abs/2305.13233 · HTML: https://mlsanity.com/paper/2305.13233/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 22 May 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)

## Built on by (most cited first, 5 of 5)

- [Efficient mapping of phase diagrams with conditional Boltzmann Generators](https://mlsanity.com/paper/2406.12378/) (2024)
- [Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Models](https://mlsanity.com/paper/2406.02313/) (2024)
- [Scalable Boltzmann Generators for equilibrium sampling of large-scale materials](https://mlsanity.com/paper/2509.25486/) (2025)
- [Energy based diffusion generator for efficient sampling of Boltzmann distributions](https://mlsanity.com/paper/2401.02080/) (2024)
- [Estimating Solvation Free Energies with Boltzmann Generators](https://mlsanity.com/paper/2512.18147/) (2025)

## Abstract (arXiv)

We present a machine-learning model based on normalizing flows that is trained to sample from the isobaric-isothermal ensemble. In our approach, we approximate the joint distribution of a fully-flexible triclinic simulation box and particle coordinates to achieve a desired internal pressure. This novel extension of flow-based sampling to the isobaric-isothermal ensemble yields direct estimates of Gibbs free energies. We test our NPT-flow on monatomic water in the cubic and hexagonal ice phases and find excellent agreement of Gibbs free energies and other observables compared with established baselines.