Source-linked AI summary
Equivariant flow-based sampling for lattice gauge theory
Gurtej Kanwar, Michael S. Albergo, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Sébastien Racanière, Danilo Jimenez Rezende, Phiala E. Shanahan
TL;DR
Lattice gauge-theory sampling suffers from critical slowing down, limiting calculations near criticality. This paper constructs gauge-invariant flow-based samplers and demonstrates substantially more efficient estimation of topological quantities in two-dimensional U(1) theory.
Problem
Critical slowing down obstructs precise sampling-based calculations in lattice gauge theories, particularly near criticality and in QCD.
Method
The paper develops invertible flow-based sampling algorithms with exactly gauge-equivariant coupling layers, producing gauge-invariant models for lattice gauge theories.
Results
The approach enables more accurate estimation of extended and topological observables than HMC and Heat Bath, including roughly 1500-fold and 200-fold greater efficiency for topological quantities, respectively.
Takeaways & Limitations
Gauge-invariant flow-based sampling can substantially reduce the critical-slowing-down burden for topological quantities in the demonstrated U(1) lattice theory.
Takeaways & Limitations
Extending the method to non-Abelian theories requires expressive invertible kernels for gauge-equivariant coupling layers, which remains future work.
Abstract
from arXiv · showhide
We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that near critical points in parameter space the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath.