HMC with Normalizing Flows

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at generating independent configurations. We show that, using a carefully constructed network architecture, our approach can be easily scaled to large lattice volumes with minimal retraining effort. The source code for our implementation is publicly available online at https://github.com/nftqcd/fthmc.

LeapfrogLayers: A Trainable Framework for Effective Topological Sampling

We introduce LeapfrogLayers, an invertible neural network architecture that can be trained to efficiently sample the topology of a 2D $U(1)$ lattice gauge theory. We show an improvement in the integrated autocorrelation time of the topological charge when compared with traditional HMC, and propose methods for scaling our model to larger lattice volumes. Our implementation is open source, and is publicly available on github at https://github.com/saforem2/l2hmc-qcd

Deep Learning Hamiltonian Monte Carlo

We generalize the Hamiltonian Monte Carlo algorithm with a stack of neural network layers and evaluate its ability to sample from different topologies in a two dimensional lattice gauge theory. We demonstrate that our model is able to successfully mix between modes of different topologies, significantly reducing the computational cost required to generated independent gauge field configurations. Our implementation is available at https://github.com/saforem2/l2hmc-qcd .