Related papers: Diffusion models for lattice gauge field simulatio…
Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
This paper develops a rigorous probabilistic framework that extends denoising diffusion models to the setting of noncommutative random variables. Building on Voiculescu's theory of free entropy and free Fisher information, we formulate…
We investigate thermal properties of a $U(1)$ lattice gauge theory in $1+1$-dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
We document our Fortran 77 code for multicanonical simulations of 4D U(1) lattice gauge theory in the neighborhood of its phase transition. This includes programs and routines for canonical simulations using biased Metropolis heatbath…
Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…
We address an old problem in lattice gauge theory - the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a…
Abelian gauge theories formulated on a space-time lattice can be used as a prototype for investigating the confinement mechanism. In U(1) lattice gauge theory it is possible to perform a dual transformation of the path integral. Simulating…
We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension…
Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updating using reweighting, or gauge fixing, respectively. These procedures do not affect the…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning…
Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…
In $\mathrm{U(1)}$ lattice gauge theory in three spacetime dimensions, confinement can be analytically shown to persist at all values of the coupling. Furthermore, the explicit predictions for the dependence of string tension $\sigma$ and…