Application of deep neural networks for computing the renormalization group flow of the two-dimensional ϕ4 field theory

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 φ4 theory, where the network successfully identifies a Wilson–Fisher-like critical point and provides an estimate of the correlation-length critical exponent.