Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks

McNaughton, Benjamin; Miloševıć, M. V.; Perali, Andrea; Pilati, Sebastiano

doi:10.1103/physreve.101.053312

Cited by 43 publications

(47 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The eigenvalue λ 0 = 1 corresponds to the stationary state and all remaining eigenvalues λ k>0 are nonnegative and smaller than 1. Due to the introduced ordering of importance ratios (9) and the fact that all w are positive, it follows that 1 > λ 1 > λ 2 > . .…”

Section: Analytic Results For the Eigenvalues Of Transition Matrixmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

Białas¹,

Korcyl²,

Stebel³

2021

Preprint

View full text Add to dashboard Cite

We provide a deepened study of autocorrelations in Neural Markov Chain Monte Carlo simulations, a version of the traditional Metropolis algorithm which employs neural networks to provide independent proposals. We illustrate our ideas using the two-dimensional Ising model. We propose several estimates of autocorrelation times, some inspired by analytical results derived for the Metropolized Independent Sampler, which we compare and study as a function of inverse temperature β. Based on that we propose an alternative loss function and study its impact on the autocorelation times. Furthermore, we investigate the impact of imposing system symmetries (Z 2 and/or translational) in the neural network training process on the autocorrelation times. Eventually, we propose a scheme which incorporates partial heat-bath updates. The impact of the above enhancements is discussed for a 16 × 16 spin system. The summary of our findings may serve as a guidance to the implementation of Neural Markov Chain Monte Carlo simulations of more complicated models.

show abstract

Section: Analytic Results For the Eigenvalues Of Transition Matrixmentioning

confidence: 99%

“…In particular, the Authors of Ref. [9] applied a similar method to spin glass models, whereas in Ref. [10] an alternative update mechanism was proposed.…”

Section: Introductionmentioning

confidence: 99%

Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

Białas¹,

Korcyl²,

Stebel³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Similarly, Ref. [192] explores the autoregressive neural networks for the improvement of classical MC simulations of the two-dimensional Edwards Anderson spin glass, a paradigmatic classical model of spin-glass theory. Likewise, Ref.…”

Section: Machine Learning Acceleration Of Monte Carlo Simulationsmentioning

confidence: 99%

Machine learning for quantum matter

Carrasquilla

2020

Advances in Physics: X

179

111

View full text Add to dashboard Cite

Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested in quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.

show abstract

“…In Mcnaughton et al . [ 23 ], autoregressive neural networks are employed to boost the efficiency of Monte Carlo methods, while Levy et al . [ 24 ] generalises Hamiltonian Monte Carlo using neural networks.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, machine learning techniques have also been utilised to enhance the efficiency of Monte Carlo sampling algorithms. In Mcnaughton et al [23], autoregressive neural networks are employed to boost the efficiency of Monte Carlo methods, while Levy et al [24] generalises Hamiltonian Monte Carlo using neural networks.…”

Section: Introductionmentioning

confidence: 99%

Quantum-Inspired Magnetic Hamiltonian Monte Carlo

2021

View full text Add to dashboard Cite

Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo algorithm that is able to generate distant proposals via the use of Hamiltonian dynamics, which are able to incorporate first-order gradient information about the target posterior. This has driven its rise in popularity in the machine learning community in recent times. It has been shown that making use of the energy-time uncertainty relation from quantum mechanics, one can devise an extension to HMC by allowing the mass matrix to be random with a probability distribution instead of a fixed mass. Furthermore, Magnetic Hamiltonian Monte Carlo (MHMC) has been recently proposed as an extension to HMC and adds a magnetic field to HMC which results in non-canonical dynamics associated with the movement of a particle under a magnetic field. In this work, we utilise the non-canonical dynamics of MHMC while allowing the mass matrix to be random to create the Quantum-Inspired Magnetic Hamiltonian Monte Carlo (QIMHMC) algorithm, which is shown to converge to the correct steady state distribution. Empirical results on a broad class of target posterior distributions show that the proposed method produces better sampling performance than HMC, MHMC and HMC with a random mass matrix.

show abstract

Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks

Cited by 43 publications

References 53 publications

Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

Machine learning for quantum matter

Quantum-Inspired Magnetic Hamiltonian Monte Carlo

Contact Info

Product

Resources

About