# Gradient-based grand canonical optimization enabled by graph neural networks with fractional atomic existence

arXiv: https://arxiv.org/abs/2507.19438 · HTML: https://mlsanity.com/paper/2507.19438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 96 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [Orb: A Fast, Scalable Neural Network Potential](https://mlsanity.com/paper/2410.22570/) (2024)
- [Symmetry-Aware Actor-Critic for 3D Molecular Design](https://mlsanity.com/paper/2011.12747/) (2020)
- [Data-driven discovery of novel 2D materials by deep generative models](https://mlsanity.com/paper/2206.12159/) (2022)
- [Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials](https://mlsanity.com/paper/2210.04225/) (2022)
- [Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials](https://mlsanity.com/paper/2312.01416/) (2023)
- [Generating stable molecules using imitation and reinforcement learning](https://mlsanity.com/paper/2107.05007/) (2021)
- [Bayesian optimization of atomic structures with prior probabilities from universal interatomic potentials](https://mlsanity.com/paper/2408.15590/) (2024)

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

- [Grand Canonical Generators](https://mlsanity.com/paper/2610.00683/) (2026)

## Abstract (arXiv)

Machine learning interatomic potentials have become an indispensable tool for materials science, enabling the study of larger systems and longer timescales. State-of-the-art models are generally graph neural networks that employ message passing to iteratively update atomic embeddings that are ultimately used for predicting properties. In this work we extend the message passing formalism with the inclusion of a continuous variable that accounts for fractional atomic existence. This allows us to calculate the gradient of the Gibbs free energy with respect to both the Cartesian coordinates of atoms and their existence. Using this we propose a gradient-based grand canonical optimization method and document its capabilities for a Cu(110) surface oxide.