Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flows

Abstract

We consider the problem of sampling lattice field configurations on a lattice from the Boltzmann distribution corresponding to some action. Since such densities arise as approximationw of an underlying functional density, we frame the task as an instance of operator learning. We propose to approximate a time-dependent neural operator whose time integral provides a mapping between the functional distributions of the free and target theories. Once a particular lattice is chosen, the neural operator can be discretized to a finite-dimensional, time-dependent vector field which in turn induces a continuous normalizing flow between finite dimensional distributions over the chosen lattice. This flow can then be trained to be a diffeormorphism between the discretized free and target theories on the chosen lattice, and, by construction, can be evaluated on different discretizations of spacetime. We experimentally validate the proposal on the 2-dimensional ${\varphi }^4$-theory to explore to what extent such operator-based flow architectures generalize to lattice sizes they were not trained on, and show that pretraining on smaller lattices can lead to a speedup over training directly on the target lattice size.

References in corpus (7)

• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Equivariant flow-based sampling for lattice gauge theory
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Sampling using $SU(N)$ gauge equivariant flows
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Learning Interpolations between Boltzmann Densities
• Towards sampling complex actions