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[2602.18482] Boltzmann Generators for Condensed Matter via Riemannian Flow Matching
Summary
This article presents a novel approach using Riemannian flow matching to enhance Boltzmann generators for sampling equilibrium distributions in condensed matter physics.
Why It Matters
The research addresses a significant gap in the application of generative modeling techniques to condensed-phase systems, potentially improving computational efficiency and accuracy in statistical mechanics. This has implications for both theoretical understanding and practical applications in materials science.
Key Takeaways
- Introduces Riemannian flow matching for improved sampling in condensed matter.
- Addresses high computational costs of density estimation in continuous normalizing flows.
- Demonstrates validation on monatomic ice, achieving accurate free energy estimates.
Physics > Computational Physics arXiv:2602.18482 (physics) [Submitted on 10 Feb 2026] Title:Boltzmann Generators for Condensed Matter via Riemannian Flow Matching Authors:Emil Hoffmann, Maximilian Schebek, Leon Klein, Frank Noé, Jutta Rogal View a PDF of the paper titled Boltzmann Generators for Condensed Matter via Riemannian Flow Matching, by Emil Hoffmann and 4 other authors View PDF HTML (experimental) Abstract:Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems remains largely unexplored. We address this by incorporating the periodicity inherent to these systems into continuous normalizing flows using Riemannian flow matching. The high computational cost of exact density estimation intrinsic to continuous normalizing flows is mitigated by using Hutchinson's trace estimator, utilizing a crucial bias-correction step based on cumulant expansion to render the stochastic estimates suitable for rigorous thermodynamic reweighting. Our approach is validated on monatomic ice, demonstrating the ability to train on systems of unprecedented size and obtain highly accurate free energy estimates without the need for traditional multistage estimators. Subjects: Computational Physics (physics.comp-ph); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Machine Learning (stat.ML) Cite...