Related papers: Multiscale Normalizing Flows for Gauge Theories
A Lorentz and gauge symmetry preserving regularization method is discussed in four dimension based on momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom of shift of the loop momentum to define the…
Flow-based generative models can face significant challenges when modeling scientific data with multiscale Fourier spectra, often producing large errors in fine-scale features. We address this problem within the framework of stochastic…
Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect…
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to…
In this paper we give a variation of the gauge procedure which employs a scalar gauge field, $B (x)$, in addition to the usual vector gauge field, $A_\mu (x)$. We study this variant of the usual gauge procedure in the context of a complex…
Theories with gauge-mediated supersymmetry breaking provide an interesting alternative to the scenario in which the soft terms of the low-energy fields are induced by gravity. These theories allow for a natural suppression of flavour…
Phenomenological evidence suggests the existence of non-trivial background fields in the QCD vacuum. On the other hand SU(3) gauge theory possessses three different classes of both non-generic and non-trivial strata that may be used as…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.
Gauge field theory of a horizontal symmetry of the group G = SU(2) X U(1) is developed so as to generalize the standard model of particle physics. All fermion and scalar fields are assumed to belong to doublets and singlets of the group in…
We develop numerical multiscale methods for viscous boundary layer flow. The goal is to derive effective boundary conditions, or wall laws, through high resolution simulations localized to the boundary coupled to a coarser simulation in the…
The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning…
We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations.…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…
The construction of a gauge field theory for elementary particles usually starts by promoting global invariance of the matter action to a local one, this in turn implying the introduction of gauge fields. We present here a procedure that…
A new approach to study the scaling behavior of the scalar theory near the Gaussian fixed point in $d$-dimensions is presented. For a class of initial data an explicit use of the Green's function of the evolution equation is made. It is…
Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…
We study the consequences of mode-collapse of normalizing flows in the context of lattice field theory. Normalizing flows allow for independent sampling. For this reason, it is hoped that they can avoid the tunneling problem of local-update…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…