A universal neural network for learning phases and criticalities

Abstract

A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical $O(3)$ model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.

arXiv comment11 pages, 18 figures

References in corpus (36)

• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Learning phase transitions by confusion
• Stochastic series expansion method with operator-loop update
• Discovering Phase Transitions with Unsupervised Learning
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Machine Learning Topological Invariants with Neural Networks
• Learning Thermodynamics with Boltzmann Machines
• Self-Learning Monte Carlo Method
• Jet Substructure Classification in High-Energy Physics with Deep Neural Networks
• Detection of phase transition via convolutional neural network
• Experimental Machine Learning of Quantum States
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Dijet resonance search with weak supervision using $\sqrt{s}=13$ TeV $pp$ collisions in the ATLAS detector
• Optimal Feedback Cooling of a Charged Levitated Nanoparticle with Adaptive Control
• Emergence of Compositional Representations in Restricted Boltzmann Machines
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Machine learning of phase transitions in the percolation and XY models
• Enhanced Higgs to ${\tau }^{+}{\tau }^{-}$ Searches with Deep Learning
• Machine learning of quantum phase transitions
• Landscape of pear-shaped even-even nuclei
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-Learning Determinantal Quantum Monte Carlo Method
• Probing hidden spin order with interpretable machine learning
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Unsupervised machine learning of quantum phase transitions using diffusion maps
• Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg Model
• Determination of the $WW$ polarization fractions in $pp\to W^{\pm }{W}^{\pm }jj$ using a deep machine learning technique
• Extending machine learning classification capabilities with histogram reweighting
• Higher-order interactions in statistical physics and machine learning: A model-independent solution to the inverse problem at equilibrium
• Machine-Learning Study using Improved Correlation Configuration and Application to Quantum Monte Carlo Simulation
• Machine learning phases and criticalities without using real data for training
• Identification of strongly interacting organic semimetals
• Classification for the universal scaling of Néel temperature and staggered magnetization density of three-dimensional dimerized spin-1/2 antiferromagnets

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