Flow-based generative models for Markov chain Monte Carlo in lattice field theory

2019/04/30 by M. S. Albergo, G. Kanwar, P. E. Shanahan · 5 citations
Computer Science · Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech #cs.LG #hep-lat

paper · pdf · doi:10.1103/physrevd.100.034515

published as Phys. Rev. D 100, 034515 (2019) · 13 pages, 7 figures; corrected normalization conventions in eqns. 20 and 23

arxiv created 2019/09/09 · arxiv updated 2019/09/10

Abstract

A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution approximating the desired Boltzmann distribution determined by the lattice action of the theory being studied. Training the model systematically improves autocorrelation times in the Markov chain, even in regions of parameter space where standard Markov chain Monte Carlo algorithms exhibit critical slowing down in producing decorrelated updates. Moreover, the model may be trained without existing samples from the desired distribution. The algorithm is compared with HMC and local Metropolis sampling for ϕ⁴ theory in two dimensions.

Cited by

• Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
• Machine Learning and Variational Algorithms for Lattice Field Theory
• Efficient Modelling of Trivializing Maps for Lattice ϕ⁴ Theory Using Normalizing Flows: A First Look at Scalability
• Introduction to Normalizing Flows for Lattice Field Theory
• Machine Learning Trivializing Maps: A First Step Towards Understanding How Flow-Based Samplers Scale Up