Few-shot machine learning in the three-dimensional Ising model

Zhang, Rui; Wei, Bin; Zhang, Dong; Zhu, Junbo; Chang, Kai

doi:10.1103/physrevb.99.094427

Cited by 22 publications

(19 citation statements)

References 62 publications

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“…For reasons of clarity, we mention that finite volume analysis has been applied in the past on results extracted via supervised machine learning[26] as well as from PCA analysis[27], however not from autoencoders.…”

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confidence: 99%

The critical temperature of the 2D-Ising model through deep learning autoencoders

et al. 2020

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We investigate deep learning autoencoders for the unsupervised recognition of phase transitions in physical systems formulated on a lattice. We focus our investigation on the 2-dimensional ferromagnetic Ising model and then test the application of the autoencoder on the anti-ferromagnetic Ising model. We use spin configurations produced for the 2-dimensional ferromagnetic and anti-ferromagnetic Ising model in zero external magnetic field. For the ferromagnetic Ising model, we study numerically the relation between one latent variable extracted from the autoencoder to the critical temperature Tc. The proposed autoencoder reveals the two phases, one for which the spins are ordered and the other for which spins are disordered, reflecting the restoration of the ℤ2 symmetry as the temperature increases. We provide a finite volume analysis for a sequence of increasing lattice sizes. For the largest volume studied, the transition between the two phases occurs very close to the theoretically extracted critical temperature. We define as a quasi-order parameter the absolute average latent variable z̃, which enables us to predict the critical temperature. One can define a latent susceptibility and use it to quantify the value of the critical temperature Tc(L) at different lattice sizes and that these values suffer from only small finite scaling effects. We demonstrate that Tc(L) extrapolates to the known theoretical value as L →∞ suggesting that the autoencoder can also be used to extract the critical temperature of the phase transition to an adequate precision. Subsequently, we test the application of the autoencoder on the anti-ferromagnetic Ising model, demonstrating that the proposed network can detect the phase transition successfully in a similar way. Graphical abstract

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confidence: 99%

The critical temperature of the 2D-Ising model through deep learning autoencoders

et al. 2020

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“…[68] and ν = 1 [69] in 2D; T c ≈ 4.511528 (6) [70] and ν ≈ 0.63012 (16) [71] in 3D. Supervised machine learning techniques have been well utilized to learn the continuous phase transition in the Ising model in both 2D [39] and 3D [72]. Here we reproduce these results using our algorithm.…”

Section: B Learning the Second-order Phase Transitionmentioning

confidence: 62%

Machine learning glass caging order parameters with an artificial nested neural network

Zhang¹,

Li²,

Jin³

et al. 2021

Preprint

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Non-equilibrium phase transitions in glassy systems are often indicated by a dramatic change of dynamics, accompanied by subtle and ambiguous structural signatures. This fact has motivated a number of recent studies attempting to pinpoint predictors that correlate structural order to dynamics in glasses, via the application of modern machine learning techniques. Here we develop a general machine learning approach, based on a two-level nested neural network, which autonomously extracts glass order parameters characterizing caging dynamics. Combining machine learning with finite-size scaling analyses, we can identify, and distinguish between, first-and second-order nonequilibrium phase transitions, demonstrated by studying melting and Gardner transitions in a simulated hard sphere glass model. Our machine learning results also suggest that the liquid-to-glass transition, as widely accepted, is a smooth crossover rather than a sharp phase transition. Our approach makes use of the power of neural networks in learning hidden dynamical features of different phases, bypassing the difficulties in defining structural order in disordered systems.

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“…In classical, solid states, and quantum physics, machine learning, both supervised and unsupervised, has quickly become a much used tool for the study of phase transitions, as witnessed by recent investigations of spin systems using techniques as diverse as principal component analysis 1 – 5 , support vector machines 6 , 7 , variational autoencoders 2 , 8 , Boltzmann machines 9 – 11 , fully connected neural networks 12 – 16 as well as convolutional neural networks 7 , 12 , 15 , 17 – 19 . The vast majority of these studies focused on systems without conserved quantities.…”

Section: Convolutional Neural Network: Phase Transition With Conservementioning

confidence: 99%

“…Machine learning methods, which encompass methods as diverse as principal component analysis 1 – 5 , support vector machines 6 , 7 , and variational autoencoders 2 , 8 , in addition to various neural network architectures 7 , 12 – 19 , have been applied to study various properties of physical systems. These models can be grouped into the two broad categories of supervised and unsupervised learning.…”

Section: Introductionmentioning

confidence: 99%

A cautionary tale for machine learning generated configurations in presence of a conserved quantity

Azizi

Pleimling

2021

Sci Rep

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We investigate the performance of machine learning algorithms trained exclusively with configurations obtained from importance sampling Monte Carlo simulations of the two-dimensional Ising model with conserved magnetization. For supervised machine learning, we use convolutional neural networks and find that the corresponding output not only allows to locate the phase transition point with high precision, it also displays a finite-size scaling characterized by an Ising critical exponent. For unsupervised learning, restricted Boltzmann machines (RBM) are trained to generate new configurations that are then used to compute various quantities. We find that RBM generates configurations with magnetizations and energies forbidden in the original physical system. The RBM generated configurations result in energy density probability distributions with incorrect weights as well as in wrong spatial correlations. We show that shortcomings are also encountered when training RBM with configurations obtained from the non-conserved Ising model.

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Few-shot machine learning in the three-dimensional Ising model

Cited by 22 publications

References 62 publications

The critical temperature of the 2D-Ising model through deep learning autoencoders

The critical temperature of the 2D-Ising model through deep learning autoencoders

Machine learning glass caging order parameters with an artificial nested neural network

A cautionary tale for machine learning generated configurations in presence of a conserved quantity

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