Sampling the Liquid-Gas Critical Point with Boltzmann Generators

TL;DR

This paper demonstrates that Boltzmann Generators, a type of invertible generative model, can effectively sample equilibrium configurations at the liquid-gas critical point, capturing critical behavior and extrapolating across phase boundaries, despite current size limitations.

Contribution

The study evaluates Boltzmann Generators at the critical point of a Lennard-Jones fluid, showing their ability to capture critical phenomena and connect generative performance with thermodynamic phase boundaries.

Findings

Boltzmann Generators capture key signatures of critical behavior.

Model performance correlates with phase boundaries.

Current limitations due to small system sizes.

Abstract

Generative models based on invertible transformations provide a physics-aware route to sample equilibrium configurations directly from the Boltzmann distribution, enabling efficient exploration of complex thermodynamic landscapes. Here, we evaluate their applicability in regions where conventional simulations suffer from severe dynamical bottlenecks, focusing on the liquid-gas critical point of a Lennard-Jones fluid. We show that Boltzmann Generators capture essential signatures of critical behavior, retain reliable performance when trained at or near criticality, and extrapolate across neighboring states of the phase diagram. An intriguing observation is that the model's efficiency metric closely traces the underlying phase boundaries, hinting at a connection between generative performance and thermodynamics. However, the approach remains limited by the small system sizes currently accessible, which suppress the large fluctuations that characterize critical phenomena. Our results delineate the current capabilities and boundaries of Boltzmann Generators in challenging regions of phase space, while pointing toward future applications in problems dominated by slow dynamics, such as glass formation and nucleation.