Sampling the liquid-gas critical point with Boltzmann generators.

Area of Science:

• Computational Physics
• Statistical Mechanics
• Machine Learning

Background:

• Generative models using invertible transformations offer a physics-informed method for sampling equilibrium states.
• These models can potentially overcome dynamical bottlenecks in conventional simulations, especially in complex thermodynamic landscapes.

Purpose of the Study:

• To assess the effectiveness of Boltzmann generators in simulating systems at their liquid-gas critical point, a region known for simulation challenges.
• To investigate the performance and extrapolation capabilities of these models when trained near or at criticality.

Main Methods:

• Utilizing generative models based on invertible transformations to simulate a Lennard-Jones fluid.
• Focusing the evaluation on the liquid-gas critical point and surrounding phase diagram regions.
• Analyzing the model's ability to capture critical behavior signatures and its performance extrapolation.

Main Results:

• Boltzmann generators successfully captured key signatures of critical behavior in the Lennard-Jones fluid.
• The models demonstrated reliable performance when trained at or near the critical point and could extrapolate to neighboring states.
• Model efficiency metrics showed a strong correlation with thermodynamic phase boundaries, suggesting a link between generative performance and system thermodynamics.

Conclusions:

• Boltzmann generators show promise for simulating systems with slow dynamics, like those near critical points.
• Current limitations include system size constraints, which hinder the capture of large fluctuations characteristic of critical phenomena.
• The study highlights the potential and boundaries of Boltzmann generators for exploring challenging regions of phase space, with future applications in areas like glass formation and nucleation.