相关论文: Improved Langevin Methods for Spin Systems

We present a new implementation of the Fourier acceleration method for Landau gauge fixing. By means of a multigrid inversion we are able to avoid the use of the fast Fourier transform. This makes the method more flexible, and well suited…

The 2nd order Runge-Kutta scheme Langevin simulation of unquenched QCD in pseudofermion method derived from our general theory shows a behaviour as a function of the Langevin step t better than the Fukugita,Oyanagi,Ukawa's scheme.

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude $S$ have $N=2S+1$ levels. Alternatively, the spin state is fully…

The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and…

We introduce an efficient Langevin method to study bilinear Fermionic Hamiltonians interacting with classical fields. Our method is suitable for very large systems and offers high accuracy. To demonstrate the method, we study complex…

Implicit score matching provides a computationally efficient approach for training diffusion models and generating high-quality samples from complex distributions. In this work, we develop a score-matching framework for SU(N) lattice gauge…

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…

We study a multigrid method for nonabelian lattice gauge theory, the time slice blocking, in two and four dimensions. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method. This…

Parallel-in-time algorithms have been successfully employed for reducing time-to-solution of a variety of partial differential equations, especially for diffusive (parabolic-type) equations. A major failing of parallel-in-time approaches to…

We present recent results on two attempts at understanding and utilizing large-scale simulations of magnetic materials. In the first study we consider massively parallel implementations on a Cray T3E of the n-fold way algorithm for…

Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…

The complex Langevin method, a numerical method used to compute the ensemble average with a complex partition function, often suffers from runaway instability. We study the regularization of the complex Langevin method via augmenting the…

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind…

This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main difficulty lies in handling the interaction between the…

Auxiliary field quantum Monte Carlo methods for Hubbard models are generally based on a Hubbard-Stratonovitch transformation where the field couples to the z-component of the spin. This transformation breaks SU(2) spin invariance. The…

Stochastic Gradient Langevin Dynamics (SGLD) ensures strong guarantees with regards to convergence in measure for sampling log-concave posterior distributions by adding noise to stochastic gradient iterates. Given the size of many practical…

We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…

By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…

A generalization of the $SU(2)$--spin systems on a lattice and their continuum limit to an arbitrary compact group $G$ is discussed. The continuum limits are, in general, non--relativistic $\sigma$--model type field theories targeted on a…

The Fourier analysis of the \emph{p}-multigrid acceleration technique is considered for a dual-time scheme applied to the advection-diffusion equation with various cycle configurations. It is found that improved convergence can be achieved…