Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory

Abstract

We present a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The procedure is embedded into a pipeline of machine learning algorithms able to detect the existence of different phases of matter, to determine the position of phase transitions and to find explicit expressions of the physical quantities by which the algorithm distinguishes between phases. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlo-sampled configurations. The method is applied to the Ising Model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the known order parameters from the decision functions of the neural networks.

References in corpus (38)

• Scikit-learn: Machine Learning in Python
• Quantum Machine Learning
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Color superconductivity in dense quark matter
• Quantum principal component analysis
• Opening the Black Box of Deep Neural Networks via Information
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Quantum Entanglement in Neural Network States
• Two Gaps Make a High Temperature Superconductor?
• Why does deep and cheap learning work so well?
• Machine learning quantum phases of matter beyond the fermion sign problem
• A Theory of the Pseudogap State of the Cuprates
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Scattering and Pairing in Cuprate Superconductors
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
• Deep-learning Top Taggers or The End of QCD?
• Quantum Loop Topography for Machine Learning
• Learning Thermodynamics with Boltzmann Machines
• Machine Learning Phases of Strongly Correlated Fermions
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• QCD phase diagram and the critical point
• The high-field phase diagram of the cuprates derived from the Nernst effect
• Detection of phase transition via convolutional neural network
• Probing many-body localization with neural networks
• Kernel methods for interpretable machine learning of order parameters
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Pure density functional for strong correlations and the thermodynamic limit from machine learning
• Functional renormalization for spontaneous symmetry breaking in the Hubbard model
• Understanding Deep Image Representations by Inverting Them
• Superconductivity from repulsive interactions in the two dimensional electron gas
• Restricted Boltzmann Machines for the Long Range Ising Models
• Sampling algorithms for validation of supervised learning models for Ising-like systems

Cited by in corpus (98)

• On scientific understanding with artificial intelligence
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Machine Learning Topological Invariants with Neural Networks
• Machine Learning in Nuclear Physics
• Machine learning vortices at the Kosterlitz-Thouless transition
• Machine Learning for Quantum Matter
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Machine learning of quantum phase transitions
• Deep Learning and AdS/CFT
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Exploring QCD matter in extreme conditions with Machine Learning
• Parameter diagnostics of phases and phase transition learning by neural networks
• Probing hidden spin order with interpretable machine learning
• Spectral Reconstruction with Deep Neural Networks
• Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase
• Machine learning action parameters in lattice quantum chromodynamics
• Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
• Measurement-induced criticality as a data-structure transition
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Learning phase transitions from dynamics
• Smallest Neural Network to Learn the Ising Criticality
• Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data
• 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
• Machine Learning of Frustrated Classical Spin Models. II. Kernel Principal Component Analysis
• The critical temperature of the 2D-Ising model through Deep Learning Autoencoders
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Stochastic normalizing flows as non-equilibrium transformations
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Interpreting machine learning of topological quantum phase transitions
• Deep Learning on the 2-Dimensional Ising Model to Extract the Crossover Region with a Variational Autoencoder
• Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system
• Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics
• Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
• Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window
• Machine Learning Application to Two-Dimensional Dzyaloshinskii-Moriya Ferromagnets
• A perspective on machine learning and data science for strongly correlated electron problems
• Machine Learning Estimators for Lattice QCD Observables
• Self-learning Monte Carlo method with Behler-Parrinello neural networks
• Deep learning of topological phase transitions from entanglement aspects
• Phase Detection with Neural Networks: Interpreting the Black Box
• Entanglement-guided architectures of machine learning by quantum tensor network
• Quantum kernels to learn the phases of quantum matter
• Phase transition encoded in neural network
• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
• Learning a Local Symmetry with Neural-Networks
• Generalization capabilities of translationally equivariant neural networks
• Probing center vortices and deconfinement in $\mathrm{SU}(2)$ lattice gauge theory with persistent homology
• Hessian-based toolbox for reliable and interpretable machine learning in physics
• Markov Chain Monte Carlo Methods in Quantum Field Theories: A Modern Primer
• Transfer learning of phase transitions in percolation and directed percolation
• Mapping out phase diagrams with generative classifiers
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Unsupervised Learning Eigenstate Phases of Matter
• Optical lattice experiments at unobserved conditions and scales through generative adversarial deep learning
• Multi-faceted machine learning of competing orders in disordered interacting systems
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Topological defects and confinement with machine learning: the case of monopoles in compact electrodynamics
• Unsupervised Machine Learning of Quenched Gauge Symmetries: A Proof-of-Concept Demonstration
• The Ising Model with Hybrid Monte Carlo
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• Variational Autoencoder Analysis of Ising Model Statistical Distributions and Phase Transitions
• Phase determination with and without deep learning
• Casimir effect with machine learning
• Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects
• Emergence of a finite-size-scaling function in the supervised learning of the Ising phase transition
• Conservation Laws and Spin System Modeling through Principal Component Analysis
• A learning algorithm with emergent scaling behavior for classifying phase transitions
• How machine learning conquers the unitary limit
• A Neural Network Perturbation Theory Based on the Born Series
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Application of the Variational Autoencoder to Detect the Critical Points of the Anisotropic Ising Model
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Machine learning classification of two-dimensional vortex configurations
• Extracting Off-Diagonal Order from Diagonal Basis Measurements
• Machine Learning Percolation Model
• Machine learning the Ising transition: A comparison between discriminative and generative approaches
• Learning phases with Quantum Monte Carlo simulation cell
• Fluctuation based interpretable analysis scheme for quantum many-body snapshots
• Phase classification in the long-range Harper model using machine learning
• Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning
• A Group-Equivariant Autoencoder for Identifying Spontaneously Broken Symmetries
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Deep Quantum Graph Dreaming: Deciphering Neural Network Insights into Quantum Experiments
• Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena
• Entanglement Clustering for ground-stateable quantum many-body states
• Interpretable Phase Detection and Classification with Persistent Homology
• Randomized-gauge test for machine learning of Ising model order parameter
• Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning
• Global exploration of phase behavior in frustrated Ising models using unsupervised learning techniques
• Deep learning of topological phase transitions from entanglement aspects: An unsupervised way
• Deep learning of thermodynamic laws from microscopic dynamics
• Neural quantum states for entanglement depth certification from randomized Pauli measurements
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo