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We study scaling properties and topological aspects of the 2--d O(3) non--linear $\sigma$--model on the lattice with the parametrized fixed point action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of the mass gap…

We consider a lattice action which forbids large fields, and which remains invariant under smooth deformations of the field. Such a "topological" action depends on one parameter, the field cutoff, but does not have a classical continuum…

The gradient flow is a valuable tool for the lattice community, with applications from scale-setting to implementing chiral fermions. Here I focus on the gradient flow as a means to suppress power-divergent mixing. Power-divergent mixing…

We apply the Symanzik improvement programme to the 4+1-dimensional local re-formulation of the gradient flow in pure $SU(N)$ lattice gauge theories. We show that the classical nature of the flow equation allows to eliminate all cutoff…

The connection is established between two different action principles for perfect fluids in the context of general relativity. For one of these actions, $S$, the fluid four--velocity is expressed as a sum of products of scalar fields and…

Machine learning methods based on normalizing flows have been shown to address important challenges, such as critical slowing-down and topological freezing, in the sampling of gauge field configurations in simple lattice field theories. A…

Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…

Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order…

Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open…

Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling…

Training deep neural networks remains computationally intensive due to the itera2 tive nature of gradient-based optimization. We propose Gradient Flow Matching (GFM), a continuous-time modeling framework that treats neural network training…

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test…

We present a new parametrization of a SU(3) fixed point (FP) gauge action using smeared ("fat") gauge links. We report on the scaling behaviour of the FP action on coarse lattices by means of the static quark-antiquark potential, the…

We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…

Sampling topological quantities in the Monte Carlo simulation of Lattice Gauge Theory becomes challenging as we approach the continuum limit of the theory. In this work, we introduce a Conditional Normalizing Flow (C-NF) model to sample…

A quantum perfect lattice action in four dimensions can be derived analytically as a renormalized trajectory when we perform a block spin transformation of monopole currents in a simple but non-trivial case of quadratic monopole…

We investigate the role of topology on the lattice determination of the $\mathrm{SU}(3)$ strong coupling renormalized via gradient flow. To deal with the topological freezing of standard local algorithms, the definition of the coupling is…

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…

We discuss a class of saddle-point configurations in SU(2) lattice gauge theory in three Euclidean dimensions. These configurations are smooth on the scale of the lattice and have an action density exhibiting localized peaks, as has been…

This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in Gradient Tracking. We provide an…