Neural Network Renormalization Group
This work addresses the challenge of performing efficient and information-preserving renormalization in statistical physics, offering a novel computational tool for physicists, though it is incremental as it builds on existing normalizing flow and RG concepts.
The paper tackles the problem of renormalization group (RG) analysis in statistical physics by introducing a variational approach using a deep generative model based on normalizing flows, which allows unbiased training and direct access to renormalized energy functions, demonstrated by identifying independent collective variables in the Ising model and enabling accelerated Monte Carlo sampling.
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural net directly maps independent Gaussian noises to physical configurations following the inverse RG flow. The model has an exact and tractable likelihood, which allows unbiased training and direct access to the renormalized energy function of the latent variables. To train the model, we employ probability density distillation for the bare energy function of the physical problem, in which the training loss provides a variational upper bound of the physical free energy. We demonstrate practical usage of the approach by identifying mutually independent collective variables of the Ising model and performing accelerated hybrid Monte Carlo sampling in the latent space. Lastly, we comment on the connection of the present approach to the wavelet formulation of RG and the modern pursuit of information preserving RG.