Locality-constrained autoregressive cum conditional normalizing flow for lattice field theory simulations

Understand

Normalizing flow-based sampling methods have been successful in tackling computational challenges traditionally associated with simulating lattice quantum field theories.

• Further works have incorporated gauge and translational invariance of the action integral in the underlying neural networks, which have led to efficient training and inference in those models.
• In this paper, we incorporate locality of the action integral which leads to simplifications to the input domain of conditional normalizing flows that sample constant time sub-lattices in an autoregressive process, dubbed local-Autoregressive Conditional Normalizing Flow (l-ACNF).
• We find that the autocorrelation times of l-ACNF models outperform an equivalent normalizing flow model on the full lattice by orders of magnitude when sampling $\phi^{4}$ theory on a 2 dimensional lattice.