Lattice quantum chromodynamics (QCD) is used to understand the behavior of subatomic particles in particle and nuclear physics.

Lattice QCD computations always begin with generation of a Markov chain of gauge field configurations. Currently, generating independent gauge configurations is a major bottleneck in the lattice QCD workflows. Development of more efficient sampling techniques is needed.

One of the fundamental problems of Markov chain Monte Carlo (MCMC) sampling algorithms is their inability to simulate theories near a critical point — a phenomenon known as critical slowing down. Because of this effect, the computational resources required to generate independent configurations increase exponentially, and the problem can quickly become insurmountable, especially for the large-dimensional theories of lattice QCD.

To combat this effect, Argonne has developed a physically inspired generalization of the ​‘l2hmc‘ algorithm that introduces transformations (parameterized by neural networks) that can be tuned to minimize the integrated autocorrelation times of physical quantities (a measure of the overall efficiency of the sampler).

Preliminary results for this model demonstrate a significant improvement compared with the current state-of-the-art techniques (e.g., Hamiltonian Monte Carlo).

Going forward, we hope to develop a better understanding of how this model can be scaled to larger lattice volumes and modified for more complicated lattice field theories, as well as how we might better incorporate physical symmetries into the model/network design.