Applications of Machine Learning to Lattice Quantum Field Theory

There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment of this approach in the future.

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 .