Generative marginal learning for finite-size molecular simulation with application to stress calculation

Abstract

We propose generative marginal learning (GML), a framework for equilibrium sampling and local observable estimation in molecular simulations. By training a conditional diffusion model on large-system simulations, GML learns the marginal distribution of a retained region, enabling configuration generation without explicitly simulating the surrounding environment or imposing periodic boundary conditions on the retained region. We derive a marginal effective potential and the associated conditional mean-force identity, which provide the basis for both denoising and force-alignment training. As an application, we estimate the spatially averaged Irving--Kirkwood stress near a vacancy defect. Numerical results demonstrate that GML substantially improves pair structure and local stress accuracy compared with small periodic molecular dynamics simulations, mitigating finite-size effects in calculating local molecular observables.

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BibTeX RIS

BibTeX

@misc{yuan2026generative,
  title = {{Generative marginal learning for finite-size molecular simulation with application to stress calculation}},
  author = {Cheng Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25105},
  eprint = {2610.25105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25105},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Generative marginal learning for finite-size molecular simulation with application to stress calculation
AU  - Cheng Yuan
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25105
UR  - https://arxiv.org/abs/2610.25105
AB  - We propose generative marginal learning (GML), a framework for equilibrium sampling and local observable estimation in molecular simulations. By training a conditional diffusion model on large-system simulations, GML learns the marginal distribution of a retained region, enabling configuration generation without explicitly simulating the surrounding environment or imposing periodic boundary conditions on the retained region. We derive a marginal effective potential and the associated conditional mean-force identity, which provide the basis for both denoising and force-alignment training. As an application, we estimate the spatially averaged Irving--Kirkwood stress near a vacancy defect. Numerical results demonstrate that GML substantially improves pair structure and local stress accuracy compared with small periodic molecular dynamics simulations, mitigating finite-size effects in calculating local molecular observables.
ER  -

Abstract

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