Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows

Abstract

We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a shallow design and incorporates the symmetries of the problem. We test our model on the ${\varphi }^4$ theory, showing that it systematically outperforms a realNVP baseline in sampling efficiency, with the difference between the two increasing for larger lattices. On the largest lattice we consider, of size $32\times 32$, we improve a key metric, the effective sample size, from 1% to 66% w.r.t. the realNVP baseline.

8 pages, 5 figures. Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021)

References in corpus (4)

• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
• Flow-based sampling for fermionic lattice field theories
• Flow-based sampling for multimodal and extended-mode distributions in lattice field theory
• Introduction to Normalizing Flows for Lattice Field Theory

Cited by in corpus (1)

• On learning higher-order cumulants in diffusion models