Related papers: Diffusion model for SU(N) gauge theories
We have applied a new noncompact, gauge-invariant, Monte Carlo method to simulate the U(1), SU(2), and SU(3) gauge theories on 8^4 and 12^4 lattices. For U(1) the Creutz ratios of the Wilson loops agree with the exact results for beta > 0.5…
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…
Machine learning (ML) is used for many earth science applications; however, traditional ML methods trained with squared errors often create blurry forecasts. Diffusion models are an emerging generative ML technique with the ability to…
We construct efficient Monte Carlo updating algorithms for two classes of pure SU(N) lattice gauge actions with non-linear dependence on the link variables. Our construction generalises the method of auxiliary variables used by Fabricius…
We study the autocorrelations of observables constructed from the topological charge density, such as the topological charge on a time slice or in a subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge theory with…
We propose an efficient framework for amortized conditional inference by leveraging exact conditional score-guided diffusion models to train a non-reversible neural network as a conditional generative model. Traditional normalizing flow…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
Forecasting future weather and climate is inherently difficult. Machine learning offers new approaches to increase the accuracy and computational efficiency of forecasts, but current methods are unable to accurately model uncertainty in…
Diffusion models have emerged as powerful learned priors for solving inverse problems. However, current iterative solving approaches which alternate between diffusion sampling and data consistency steps typically require hundreds or…
Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…
Far-from-equilibrium dynamics of SU(2) gauge theory with Wilson fermions is studied in 1+1 space-time dimensions using a real-time lattice approach. Lattice improved Hamiltonians are shown to be very efficient in simulating Schwinger pair…
We study the theoretical foundations of composition in diffusion models, with a particular focus on out-of-distribution extrapolation and length-generalization. Prior work has shown that composing distributions via linear score combination…
For a system near a second order phase transition, the probability distribution for the order parameter can be given a finite size scaling form. This fact is used to compare the finite temperature phase transition for the Wilson lines in…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
In order to investigate the features of the classical approximation at high temperatures for real time correlation functions, the plasmon frequencies and damping rates were recently computed numerically in the SU(2)+Higgs model and in the…
This thesis is concerned with two topics in Hamiltonian lattice gauge theory: improvement and the application of analytic techniques. On the topic of improvement, we develop a direct method for improving lattice Hamiltonians for gluons, in…