Exploring Generative Networks for Manifolds with Non-Trivial Topology

• DOI: 10.48550/arxiv.2502.02127
• Publication Date: 2025-02-12
• Authors: Chen, Shiyang; Aarts, Gert; Lucini, Biagio
• Keywords: High Energy Physics - Lattice; High Energy Physics - Lattice (hep-lat); FOS: Physical sciences

10 pages, 7 figures. Talk presented at the 41th International Symposium on Lattice Field Theory (Lattice 2024), July 28th to August 3rd, 2024, the University of Liverpool, United Kingdom<br/>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.<br/>