Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory

Abstract

We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the method on two examples. The first one is a one-dimensional Gaussian model, where RGFlow is shown to learn the classical decimation rule. The second is the two-dimensional phi^4 theory, where the network successfully identifies a Wilson-Fisher-like critical point and provides an estimate of the correlation-length critical exponent.

13 pages, 5 figures

References in corpus (4)

• Deep Learning of Atomically Resolved Scanning Transmission Electron Microscopy Images: Chemical Identification and Tracking Local Transformations
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• Hybrid Machine Learning for Scanning Near-field Optical Spectroscopy
• Investigations in 1+1 dimensional lattice ${\varphi }^4$ theory