Multi-Lattice Sampling of Quantum Field Theories via Neural
Operator-based Flows
- URL: http://arxiv.org/abs/2401.00828v3
- Date: Wed, 17 Jan 2024 14:17:41 GMT
- Title: Multi-Lattice Sampling of Quantum Field Theories via Neural
Operator-based Flows
- Authors: B\'alint M\'at\'e, Fran\c{c}ois Fleuret
- Abstract summary: We consider the problem of sampling discrete field configurations from the Boltzmann distribution.
We frame the task as an instance of operator learning.
We show that pretraining on smaller lattices can lead to speedup over training only a target lattice size.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider the problem of sampling discrete field configurations $\phi$ from
the Boltzmann distribution $[d\phi] Z^{-1} e^{-S[\phi]}$, where $S$ is the
lattice-discretization of the continuous Euclidean action $\mathcal S$ of some
quantum field theory. Since such densities arise as the approximation of the
underlying functional density $[\mathcal D\phi(x)] \mathcal Z^{-1} e^{-\mathcal
S[\phi(x)]}$, we frame the task as an instance of operator learning. In
particular, we propose to approximate a time-dependent operator $\mathcal V_t$
whose time integral provides a mapping between the functional distributions of
the free theory $[\mathcal D\phi(x)] \mathcal Z_0^{-1} e^{-\mathcal
S_{0}[\phi(x)]}$ and of the target theory $[\mathcal D\phi(x)]\mathcal
Z^{-1}e^{-\mathcal S[\phi(x)]}$. Whenever a particular lattice is chosen, the
operator $\mathcal V_t$ can be discretized to a finite dimensional,
time-dependent vector field $V_t$ 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 $[d\phi] Z_0^{-1} e^{-S_{0}[\phi]}$,
$[d\phi] Z^{-1}e^{-S[\phi]}$. We run experiments on the $\phi^4$-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 speedup over training only a target lattice size.
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