A scalable flow-based approach to mitigate topological freezing

• URL: http://arxiv.org/abs/2601.20708v1
• Date: Wed, 28 Jan 2026 15:40:46 GMT
• Title: A scalable flow-based approach to mitigate topological freezing
• Authors: Claudio Bonanno, Andrea Bulgarelli, Elia Cellini, Alessandro Nada, Dario Panfalone, Davide Vadacchino, Lorenzo Verzichelli,
• Abstract summary: We present a flow-based strategy to remove topological artifacts from Markov Chain Monte Carlo simulations.<n>The strategy is based on a Normalizing Flow (SNF) that alternates non-equilibrium Monte Carlo updates with localized, stout-equivariant defect layers.<n>We show that defect SNFs achieve better performances than reproducing non-equilibrium methods at comparable cost.
• Score: 34.54607280864912
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As lattice gauge theories with non-trivial topological features are driven towards the continuum limit, standard Markov Chain Monte Carlo simulations suffer for topological freezing, i.e., a dramatic growth of autocorrelations in topological observables. A widely used strategy is the adoption of Open Boundary Conditions (OBC), which restores ergodic sampling of topology but at the price of breaking translation invariance and introducing unphysical boundary artifacts. In this contribution we summarize a scalable, exact flow-based strategy to remove them by transporting configurations from a prior with a OBC defect to a fully periodic ensemble, and apply it to 4d SU(3) Yang--Mills theory. The method is based on a Stochastic Normalizing Flow (SNF) that alternates non-equilibrium Monte Carlo updates with localized, gauge-equivariant defect coupling layers implemented via masked parametric stout smearing. Training is performed by minimizing the average dissipated work, equivalent to a Kullback--Leibler divergence between forward and reverse non-equilibrium path measures, to achieve more reversible trajectories and improved efficiency. We discuss the scaling with the number of degrees of freedom affected by the defect and show that defect SNFs achieve better performances than purely stochastic non-equilibrium methods at comparable cost. Finally, we validate the approach by reproducing reference results for the topological susceptibility.

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