Boltzmann Generators for Condensed Matter via Riemannian Flow Matching
This addresses sampling challenges in statistical mechanics for condensed matter physics, representing a novel application rather than an incremental improvement.
The paper tackles the problem of sampling equilibrium distributions in condensed-phase systems by incorporating periodicity into continuous normalizing flows using Riemannian flow matching, achieving highly accurate free energy estimates for monatomic ice without traditional multistage estimators.
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.