Testing algorithms for critical slowing down

Cossu, Guido; Boyle, Peter; Christ, Norman H.; Jung, Chulwoo; Jüttner, Andreas; Sanfilippo, Francesco

doi:10.1051/epjconf/201817502008

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…For some models, algorithms have been found which significantly reduce or eliminate this slowing down [4][5][6][7][8][9][10][11], enabling efficient simulation. For field theories, a number of methods have been proposed to circumvent critical slowing down by variations of Hybrid Monte Carlo (HMC) techniques [12][13][14][15], multi-scale updating procedures [16][17][18], open boundary conditions or non-orientable manifolds [19][20][21], metadynamics [22], and machine learning tools [23,24]. In important classes of theories, however, critical slowing down remains limiting; for example, in lattice formulations of Quantum Chromodynamics (QCD, the piece of the Standard Model describing the strong nuclear force) it is a major barrier to simulations at the fine lattice spacings required for precise control of the continuum limit.…”

Section: Introductionmentioning

confidence: 99%

Flow-based generative models for Markov chain Monte Carlo in lattice field theory

2019

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A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution approximating the desired Boltzmann distribution determined by the lattice action of the theory being studied. Training the model systematically improves autocorrelation times in the Markov chain, even in regions of parameter space where standard Markov chain Monte Carlo algorithms exhibit critical slowing down in producing decorrelated updates. Moreover, the model may be trained without existing samples from the desired distribution. The algorithm is compared with HMC and local Metropolis sampling for φ 4 theory in two dimensions.

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Section: Introductionmentioning

confidence: 99%

Flow-based generative models for Markov chain Monte Carlo in lattice field theory

2019

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“…[17] for gauge theories with dynamical fermions, and in both cases the topological tunneling rate is expected to become exponentially suppressed farther toward the continuum limit. In addition to multiscale thermalization, a variety of other approaches have been proposed and studied for addressing topological freezing [18][19][20][21][22] and critical slowing down [23,24] in lattice QCD [25].…”

Section: Introductionmentioning

confidence: 99%

Scaling properties of multiscale equilibration

Detmold

Endres

2018

Phys. Rev. D

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We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on nontopological long-distance observables in pure SUð3Þ gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.

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“…Lattice gauge theory formulates the Feynman path integral for QCD as a statistical mechanical sampling of the related Euclidean space path integral. The sampling is performed by Markov chain Monte Carlo (MCMC) sampling, using forms of the hybrid Monte Carlo (HMC) algorithm [11][12][13][14][15][16]. The partition function of QCD is sampled through the introduction of auxiliary momentum (π) and pseudofermion (φ) integrals, Z = dπ dφ dU e −π 2 /2 e −S G [U ] e −φ * (D † D) −1 φ .…”

Section: Lattice Qcd and Algorithmsmentioning

confidence: 99%

Lattice QCD and the Computational Frontier

Boyle,

Bollweg,

Brower

et al. 2022

Preprint

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The search for new physics requires a joint experimental and theoretical effort. Lattice QCD is already an essential tool for obtaining precise model-free theoretical predictions of the hadronic processes underlying many key experimental searches, such as those involving heavy flavor physics, the anomalous magnetic moment of the muon, nucleon-neutrino scattering, and rare, second-order electroweak processes. As experimental measurements become more precise over the next decade, lattice QCD will play an increasing role in providing the needed matching theoretical precision. Achieving the needed precision requires simulations with lattices with substantially increased resolution. As we push to finer lattice spacing we encounter an array of new challenges. They include algorithmic and software-engineering challenges, challenges in computer technology and design, and challenges in maintaining the necessary human resources. In this white paper we describe those challenges and discuss ways they are being dealt with. Overcoming them is key to supporting the community effort required to deliver the needed theoretical support for experiments in the coming decade.

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Testing algorithms for critical slowing down

Cited by 9 publications

References 19 publications

Flow-based generative models for Markov chain Monte Carlo in lattice field theory

Flow-based generative models for Markov chain Monte Carlo in lattice field theory

Scaling properties of multiscale equilibration

Lattice QCD and the Computational Frontier

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