相关论文: Improved Langevin Methods for Spin Systems

The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional…

It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…

This paper introduces Stochastic Gradient Langevin Boosting (SGLB) - a powerful and efficient machine learning framework that may deal with a wide range of loss functions and has provable generalization guarantees. The method is based on a…

We address the problem of the gauge fixing versus Gribov copies in lattice gauge theories. For the Landau gauge, results show that a suitable combination of evolutionary algorithms with traditional steepest descent methods identifies the…

Stochastic Gradient Langevin Dynamics infuses isotropic gradient noise to SGD to help navigate pathological curvature in the loss landscape for deep networks. Isotropic nature of the noise leads to poor scaling, and adaptive methods based…

In this paper, an error analysis of a three steps two level Galekin finite element method for the two dimensional transient Navier-Stokes equations is discussed. First of all, the problem is discretized in spatial direction by employing…

We present an application of the standard Langevin dynamics to the problem of weak coupling perturbative expansions for Lattice QCD. This method can be applied to the computation of the most general observables. In this preliminary work we…

We present an algorithm that quickly finds falsifying inputs for hybrid systems, i.e., inputs that steer the system towards violation of a given temporal logic requirement. Our method is based on a probabilistically directed search of an…

We make a comparative analysis of some recent one-dimensional Langevin models of the acceleration of a Lagrangian fluid particle in developed turbulent flow. The class of models characterized by random intensities of noises (RIN models)…

We extend the inequality of Tomboulis and Yaffe in SU(2) lattice gauge theory (LGT) to SU(N) LGT and to general classical spin systems, by use of reflection positivity. Basically the inequalities guarantee that a system in a box that is…

Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…

We study learning to learn for regression problems through the lens of hyperparameter tuning. We propose the Langevin Gradient Descent Algorithm (LGD), which approximates the mean of the posterior distribution defined by the loss function…

We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…

A multigrid method for the Stokes system discretized with an Hdiv-conforming discontinuous Galerkin method is presented. It acts on the combined velocity and pressure spaces and thus does not need a Schur complement approximation. The…

In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to…

Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…

This paper presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles,…

Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time…

The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…

Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…