Flow-based sampling for fermionic lattice field theories

Abstract

Critical slowing down and topological freezing severely hinder Monte Carlo sampling of lattice field theories as the continuum limit is approached. Recently, significant progress has been made in applying a class of generative machine learning models, known as "flow-based" samplers, to combat these issues. These generative samplers also enable promising practical improvements in Monte Carlo sampling, such as fully parallelized configuration generation. These proceedings review the progress towards this goal and future prospects of the method.

Prospects for precise predictions of $a_μ$ in the Standard Model

“…Further methodological developments, for example, to more efficiently generate gauge field ensembles with small lattice spacings and large volumes (see, for example, Refs. [225][226][227][228][229]) as well as improved statistical noise reduction (see, for example, Refs. [230][231][232]) would further enhance the impact of these future computational resources on the precision of the lattice QCD results.…”

Flow-based sampling in the lattice Schwinger model at criticality

“…To do so, an ensemble of 1.2 × 10 7 configurations is produced using these augmentation hits alternated with HMC steps. The baseline results are estimated to be ψψ = 1.50918 (9), χ Q = 0.003875(4).…”

“…As the system is tuned towards criticality, increasingly large potential barriers suppress tunneling between sectors. In contrast, emerging flow-based sampling algorithms [5][6][7][8][9][10][11] propose random hops throughout configuration space, unaffected by density barriers. While topological freezing presents a well-known obstacle to extending the reach of stateof-the-art lattice QCD calculations [1,12,13], promising results of flow-based samplers in theories without fermions [6,7,14,15], without gauge fields [9], or away from criticality [16] suggest that these methods may provide a path towards mitigating freezing in this context.…”

“…Out of the four treatments in Ref. [9], here we consider a "marginal sampler" using exact evaluation of the fermion determinant. This means that our model describes only gauge degrees of freedom, and we compute Eq.…”

“…The sampling approach here employs exact evaluation of the fermion determinant, but more scalable approaches will be needed for larger volumes and theories in higher dimensions; extending the machine-learned stochastic determinant estimators of Ref. [9] to lattice gauge theories presents a promising opportunity. If the success demonstrated here for the Schwinger model can be extended to other theories, and in particular at scale, it will have widespread impact across nuclear and particle physics, as well as in condensed matter applications.…”