Flow based method helps sample topological features in physics simulations
Ergodic topology sampling toward the continuum with Stochastic Normalizing Flows
Machine Learning
Summary
Some physics simulations struggle to explore certain important features because they get stuck, a problem called topological freezing. The authors tested a new numerical method that uses a flow-based technique combined with special boundary conditions to fix this problem. Their results show this approach keeps the exploration balanced even in very detailed simulations. This improvement can make future physics simulations more reliable and efficient at capturing complex behaviors.
What this means in practice
- •For computational physicists: Enhance lattice gauge theory simulations by reducing sampling problems related to topology, allowing longer and more accurate calculations.
- •For machine learning engineers: Incorporate flow-based models designed for ergodic sampling in complex scientific simulations to improve sampling efficiency over challenging state spaces.
Authors
Claudio Bonanno, Andrea Bulgarelli, Elia Cellini, Alessandro Nada, Dario Panfalone, Davide Vadacchino, Lorenzo Verzichelli
Abstract
In this work we provide numerical evidence that topological freezing in $\mathrm{SU}(3)$ Yang-Mills theory can be mitigated with a flow-based approach, as tested at lattice spacings as fine as 0.03~fm. We do so by analyzing the scaling of the costs of a computational strategy based on the combination of open boundary conditions and Stochastic Normalizing Flows. We show that the integrated autocorrelation time of the squared topological charge and the statistical uncertainty on the topological susceptibility remain under control throughout the explored parameter range with currently available computational resources. This marks an important step toward the use of even more efficient flow-based architectures for ergodic sampling of topology in state-of-the-art lattice gauge theory calculations.