Neural Network Renormalization Group.

Area of Science:

• Statistical Physics
• Machine Learning
• Computational Physics

Background:

• Renormalization Group (RG) methods are crucial for understanding systems across scales.
• Generative models offer powerful tools for complex data representation.
• Developing efficient sampling techniques is vital for computational physics.

Purpose of the Study:

• To develop a novel variational renormalization group (RG) approach using a reversible generative model.
• To enable direct access to renormalized energy functions and identify independent collective variables.
• To accelerate sampling methods in complex physical systems.

Main Methods:

• A hierarchical generative model with reversible transformations from physical to latent space.
• Exact and tractable likelihood for unbiased training and direct access to latent renormalized energy.
• Probability density distillation for training loss as a variational upper bound on free energy.

Main Results:

• Successfully identified mutually independent collective variables for the Ising model.
• Demonstrated accelerated hybrid Monte Carlo sampling in the latent space.
• Established a connection between the generative model and wavelet-based RG formulations.

Conclusions:

• The proposed variational RG approach provides an effective framework for analyzing complex physical systems.
• This method facilitates the discovery of relevant degrees of freedom and enhances computational efficiency.
• The approach aligns with modern research on information-preserving RG transformations.