Scalable Boltzmann generators for equilibrium sampling of large-scale materials
6 affiliations
- 1Department of Physics, Freie Universität Berlin, Berlin, Germany. [email protected]
- 2Department of Chemistry, Rice University, Houston, TX, USA
- 3Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
- 4Department of Physics, Freie Universität Berlin, Berlin, Germany
- 5Microsoft Research AI for Science, Berlin, Germany
- 6Initiative for Computational Catalysis, Flatiron Institute, New York, NY, USA
Abstract
Generating equilibrium ensembles of structures is essential for modeling molecules and materials, yet traditional simulators like molecular dynamics suffer from limited sampling efficiency. Boltzmann Generators introduced the concept of one-shot deep learning for equilibrium sampling, but scalability to large systems has remained a major challenge. Here, we overcome this scaling limitation with a Boltzmann Generator architecture that can model large materials systems. Our approach combines augmented coupling flows with graph neural networks to exploit local environments, enabling energy-based training and rapid inference. Compared to previous designs, it trains faster, uses fewer resources, and achieves superior sampling efficiency. Crucially, it transfers to much larger system sizes, allowing efficient sampling of materials with simulation cells exceeding a thousand atoms. We demonstrate its capabilities on Lennard-Jones crystals, mW water ice phases, and the silicon phase diagram, producing accurate equilibrium ensembles and free energies across scales where finite-size effects vanish.
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BibTeX
@article{schebek2026scalable,
title = {{Scalable Boltzmann generators for equilibrium sampling of large-scale materials}},
author = {Maximilian Schebek and Frank Noé and Jutta Rogal},
journal = {Nature Communications},
year = {2026},
month = jun,
doi = {10.1038/s41467-026-73900-9},
url = {https://doi.org/10.1038/s41467-026-73900-9},
note = {CC BY},
}
RIS
TY - JOUR
TI - Scalable Boltzmann generators for equilibrium sampling of large-scale materials
AU - Maximilian Schebek
AU - Frank Noé
AU - Jutta Rogal
PY - 2026
DA - 2026/06/05
JO - Nature Communications
DO - 10.1038/s41467-026-73900-9
UR - https://doi.org/10.1038/s41467-026-73900-9
AB - Generating equilibrium ensembles of structures is essential for modeling molecules and materials, yet traditional simulators like molecular dynamics suffer from limited sampling efficiency. Boltzmann Generators introduced the concept of one-shot deep learning for equilibrium sampling, but scalability to large systems has remained a major challenge. Here, we overcome this scaling limitation with a Boltzmann Generator architecture that can model large materials systems. Our approach combines augmented coupling flows with graph neural networks to exploit local environments, enabling energy-based training and rapid inference. Compared to previous designs, it trains faster, uses fewer resources, and achieves superior sampling efficiency. Crucially, it transfers to much larger system sizes, allowing efficient sampling of materials with simulation cells exceeding a thousand atoms. We demonstrate its capabilities on Lennard-Jones crystals, mW water ice phases, and the silicon phase diagram, producing accurate equilibrium ensembles and free energies across scales where finite-size effects vanish.
SN - 2041-1723
ER -