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Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult…
The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…
Stochastic linear modelling proposed in Tissot, M\'emin & Cavalieri (J. Fluid Mech., vol. 912, 2021, A51) is based on classical conservation laws subject to a stochastic transport. Once linearised around the mean flow and expressed in the…
We describe and numerically test the velocity-dependent one-scale (VOS) string evolution model, a simple analytic approach describing a string network with the averaged correlation length and velocity. We show that it accurately reproduces…
We show that the Nambu-Goto string, and its higher dimensional generalizations, can be quantized, in the sense of an effective theory, in any dimension of the target space. The crucial point is to consider expansions around classical string…
Recent results have demonstrated that samplers constructed with flow-based generative models are a promising new approach for configuration generation in lattice field theory. In this paper, we present a set of training- and…
In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carath\'eodory formulation of…
Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow…
A homogenised model is developed to describe the interaction between aligned strings and an incompressible, viscous, Newtonian fluid. In the case of many strings, the ratio of string separation to domain width gives a small parameter which…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…
In previous work we used magnetic SU(N) gauge theory with adjoint representation Higgs scalars to describe the long distance quark-antiquark interaction in pure Yang-Mills theory, and later to obtain an effective string theory. The…
We study the Z(2) lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop…
Flow-matching models provide a powerful framework for various applications, offering efficient sampling and flexible probability path modeling. These models are characterized by flows with low curvature in learned generative trajectories,…
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…
The U(1) lattice gauge theory in three dimensions is a perfect laboratory to study the properties of the confining string. On the one hand, thanks to the mapping to a Coulomb gas of monopoles, the confining properties of the model can be…
In this paper, we propose an approach for simulating wall-bounded incompressible turbulent flows by integrating the technology of random vortex method with the core principles of large-eddy simulations (LES). In particular, we employ the…
Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In…
The low-energy effective action on long string-like objects in quantum field theory, such as confining strings, includes the Nambu-Goto action and then higher-derivative corrections. This action is diffeomorphism-invariant, and can be…