Generative sampling with physics-informed kernels

TL;DR

This paper introduces a physics-informed generative network leveraging renormalisation group flows and differential equations to improve Monte-Carlo sampling in lattice field theories, enabling better out-of-domain generalization.

Contribution

It presents a novel architecture that uses analytically known kernels and differential equations for layerwise propagation, enhancing generative sampling in physics-based models.

Findings

Successfully applied to scalar field theories

Demonstrates improved out-of-domain sampling

Provides a new framework for physics-informed generative models

Abstract

We construct a generative network for Monte-Carlo sampling in lattice field theories and beyond, for which the learning of layerwise propagation is done and optimised independently on each layer. The architecture uses physics-informed renormalisation group flows that provide access to the layerwise propagation step from one layer to the next in terms of a simple first order partial differential equation for the respective renormalisation group kernel through a given layer. Thus, it transforms the generative task into that of solving once the set of independent and linear differential equations for the kernels of the transformation. As these equations are analytically known, the kernels can be refined iteratively. This allows us to structurally tackle out-of-domain problems generally encountered in generative models and opens the path to further optimisation. We illustrate the practical feasibility of the architecture within simulations in scalar field theories.