Detection of phase transition via convolutional neural network

Abstract

We design a Convolutional Neural Network (CNN) which studies correlation between discretized inverse temperature and spin configuration of 2D Ising model and show that it can find a feature of the phase transition without teaching any a priori information for it. We also define a new order parameter via the CNN and show that it provides well approximated critical inverse temperature. In addition, we compare the activation functions for convolution layer and find that the Rectified Linear Unit (ReLU) is important to detect the phase transition of 2D Ising model.

7 pages, 10 figures

References in corpus (10)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Discovering Phase Transitions with Unsupervised Learning
• Machine learning quantum phases of matter beyond the fermion sign problem
• An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
• Phenomenological Review on Quark-Gluon Plasma: Concepts vs. Observations
• Machine learning for many-body physics: The case of the Anderson impurity model
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Machine learning for many-body physics: efficient solution of dynamical mean-field theory

Cited by in corpus (95)

• Machine learning and the physical sciences
• A high-bias, low-variance introduction to Machine Learning for physicists
• Quantum convolutional neural network for classical data classification
• Machine learning quantum phases of matter beyond the fermion sign problem
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Machine Learning Topological Invariants with Neural Networks
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Machine Learning for Quantum Matter
• Kernel methods for interpretable machine learning of order parameters
• Solving the Bose-Hubbard model with machine learning
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Solving frustrated quantum many-particle models with convolutional neural networks
• Machine learning of quantum phase transitions
• Deep Learning and AdS/CFT
• Machine Learning for Condensed Matter Physics
• Exploring QCD matter in extreme conditions with Machine Learning
• Deep Learning Topological Invariants of Band Insulators
• Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow
• Self-learning Monte Carlo with Deep Neural Networks
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Smallest Neural Network to Learn the Ising Criticality
• Applications of neural networks to the studies of phase transitions of two-dimensional Potts models
• Machine Learning as a universal tool for quantitative investigations of phase transition
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Thermodynamics and Feature Extraction by Machine Learning
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Mapping distinct phase transitions to a neural network
• Method to solve quantum few-body problems with artificial neural networks
• Quantum field-theoretic machine learning
• Machine-learning-based identification for initial clustering structure in relativistic heavy-ion collisions
• Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transitions in the q-state clock models
• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
• Extending machine learning classification capabilities with histogram reweighting
• Deep Neural Network Detects Quantum Phase Transition
• Machine Learning Application to Two-Dimensional Dzyaloshinskii-Moriya Ferromagnets
• A perspective on machine learning and data science for strongly correlated electron problems
• Extracting Critical Exponent by Finite-Size Scaling with Convolutional Neural Networks
• Self-learning Monte Carlo method with Behler-Parrinello neural networks
• Generative models for sampling and phase transition indication in spin systems
• Phase Detection with Neural Networks: Interpreting the Black Box
• Deep learning of topological phase transitions from entanglement aspects
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Phase transition encoded in neural network
• Approximating power of machine-learning ansatz for quantum many-body states
• Deep neural networks for direct, featureless learning through observation: the case of 2d spin models
• Self-organizing maps as a method for detecting phase transitions and phase identification
• Identifying Product Order with Restricted Boltzmann Machines
• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
• A Neural Networks study of the phase transitions of Potts model
• Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networks
• Towards meaningful physics from generative models
• A Deep Learning Functional Estimator of Optimal Dynamics for Sampling Large Deviations
• Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transition and the second-order phase transition in the XXZ models
• Machine learning generated configurations in presence of a conserved quantity: a cautionary tale
• Can a CNN trained on the Ising model detect the phase transition of the $q$-state Potts model?
• Machine learning phases and criticalities without using real data for training
• Visualizing Neural Network Developing Perturbation Theory
• Bayesian Optimization of Bose-Einstein Condensates
• Neural network-based preprocessing to estimate the parameters of the X-ray emission of a single-temperature thermal plasma
• RG inspired Machine Learning for lattice field theory
• Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice
• Study of phase transition of Potts model with Domain Adversarial Neural Network
• Machine learning phase transitions of the three-dimensional Ising universality class
• Machine learning as an improved estimator for magnetization curve and spin gap
• Learning to find order in disorder
• Machine learning algorithms based on generalized Gibbs ensembles
• Variational Tensor Neural Networks for Deep Learning
• Probing Criticality in Quantum Spin Chains with Neural Networks
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• Machine learning of phases and structures for model systems in physics
• Phase determination with and without deep learning
• Emergence of a finite-size-scaling function in the supervised learning of the Ising phase transition
• Machine learning phases of an Abelian gauge theory
• Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects
• Investigating Network Parameters in Neural-Network Quantum States
• Thermodynamics of the Ising model encoded in restricted Boltzmann machines
• Data-driven discovery of self-similarity using neural networks
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Learning What a Machine Learns in a Many-Body Localization Transition
• Machine Learning Percolation Model
• Logical Reasoning for Revealing the Critical Temperature through Deep Learning of Configuration Ensemble of Statistical Systems
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Comments on the minimal training set for CNN: a case study of the frustrated $J_1$-$J_2$ Ising model on the square lattice
• A universal neural network for learning phases and criticalities
• Interpretable Phase Detection and Classification with Persistent Homology
• Deep learning of topological phase transitions from entanglement aspects: An unsupervised way
• Feature extraction of machine learning and phase transition point of Ising model
• Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning
• Machine-Learning Detection of the Berezinskii-Kosterlitz-Thouless Transitions
• Machine learning in physics: The pitfalls of poisoned training sets
• Quantum-classical simulation of quantum field theory by quantum circuit learning
• Deep learning of thermodynamic laws from microscopic dynamics
• New Metric Formulas that Include Measurement Errors in Machine Learning for Natural Sciences
• Identifying phase transitions in physical systems with neural networks: a neural architecture search perspective