Speaker
Description
We address the signal-to-noise problem in lattice field theory by framing it as a task in variance-optimal transport. The degradation of the signal-to-noise ratio is shown to result from poor overlap between the configuration distribution and the target distribution in a source reweighting scheme. We introduce an infinitesimal transport map and derive a perturbative expansion of the KL divergence to determine the optimal transport field. This expansion reveals a connection to Stein geometry and allows us to recast the optimisation problem as a Poisson equation. A formal solution is provided using a stochastic method, thereby establishing a link to linear response theory. Finally, we present preliminary numerical results for scalar lattice field theories.