Related papers: HMC and gradient flow with machine-learned classic…
We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and…
Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up…
We introduce a new Monte Carlo method for pure gauge theories. It is not intended for use with dynamical fermions. It belongs to the class of Local Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the action by…
There exist lattice actions which give cut--off independent physical predictions even on coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in addition, the classical equations have scale invariant…
We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while…
The recipe behind the success of deep learning has been the combination of neural networks and gradient-based optimization. Understanding the behavior of gradient descent however, and particularly its instability, has lagged behind its…
We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We…
We enable the automatic construction of Hybrid Monte Carlo (HMC) forces in lattice gauge theory by performing reverse-mode automatic differentiation at the level of optimized LLVM intermediate representation, making the approach applicable…
We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a…
The so-called trivializing flows were proposed to speed up Hybrid Monte Carlo simulations, where the Wilson flow was used as an approximation of a trivializing map, a transformation of the gauge fields which trivializes the theory. It was…
A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…
Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of…
We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes, and naturally live on a…
Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…
We construct a perfect lattice action for staggered fermions by blocking from the continuum. The locality, spectrum and pressure of such perfect staggered fermions are discussed. We also derive a consistent fixed point action for free gauge…
We study the running of the coupling in SU(2) gauge theory with 8 massless fundamental representation fermion flavours, using the gradient flow method with the Schr\"odinger functional boundary conditions. Gradient flow allows us to measure…
Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the…
Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in…
We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional $U(1)$ gauge theory with and without fermion content. This algorithm includes reversible jumps between…
Lattice gauge theories coupled to fermionic matter account for many interesting phenomena in both high energy physics and condensed matter physics. Certain regimes, e.g. at finite fermion density, are difficult to simulate with traditional…