Exploring Generative Networks for Manifolds with Non-Trivial Topology

TL;DR

This paper introduces a novel generative method inspired by GFlowNets to efficiently explore configuration spaces with complex topology, improving sampling in lattice field theory simulations.

Contribution

The paper presents a new generative approach based on GFlowNets that effectively samples non-trivial topological configurations in lattice field theories.

Findings

Efficient exploration of ergodic configuration manifolds.

Successful application to triple ring models.

Improved sampling of non-trivial topologies.

Abstract

The expressive power of neural networks in modelling non-trivial distributions can in principle be exploited to bypass topological freezing and critical slowing down in simulations of lattice field theories. Some popular approaches are unable to sample correctly non-trivial topology, which may lead to some classes of configurations not being generated. In this contribution, we present a novel generative method inspired by a model previously introduced in the ML community (GFlowNets). We demonstrate its efficiency at exploring ergodically configuration manifolds with non-trivial topology through applications such as triple ring models and two-dimensional lattice scalar field theory.