Generative models for sampling and phase transition indication in spin systems

Abstract

Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data distributions. Motivated by their ability to generate images that look realistic to the human eye, we here study generative adversarial networks (GANs) as tools to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters, such as temperature. We propose ways to efficiently represent the physical states, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. We present a detailed evaluation of the various modifications, using the two-dimensional XY model as an example, and find considerable improvements in our proposed implicit generative model. It is also shown that the model can reliably generate samples in the vicinity of the phase transition, even when it has not been trained in the critical region. On top of using the samples generated by the model to capture the phase transition via evaluation of observables, we show how the model itself can be employed as an unsupervised indicator of transitions, by constructing measures of the model's susceptibility to changes in tuning parameters.

arXiv comment15 pages, 4 figures, 3 tables

References in corpus (47)

• Conditional Generative Adversarial Nets
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Interpretable machine learning: definitions, methods, and applications
• Tutorial on Variational Autoencoders
• A high-bias, low-variance introduction to Machine Learning for physicists
• Quantum Monte Carlo with Directed Loops
• Cluster Algorithm for Vertex Models
• Identifying topological order through unsupervised machine learning
• The Loop Algorithm
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Learning Thermodynamics with Boltzmann Machines
• Self-Learning Monte Carlo Method
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Learning in Implicit Generative Models
• Machine learning vortices at the Kosterlitz-Thouless transition
• Detection of phase transition via convolutional neural network
• Unsupervised machine learning and band topology
• Machine learning meets quantum physics
• Integrating Neural Networks with a Quantum Simulator for State Reconstruction
• Asymptotically unbiased estimation of physical observables with neural samplers
• CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks
• Regressive and generative neural networks for scalar field theory
• Unsupervised Manifold Clustering of Topological Phononics
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Deep Learning the Ising Model Near Criticality
• Self-Learning Determinantal Quantum Monte Carlo Method
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Quantum Fidelity and Thermal Phase Transitions
• Unsupervised identification of topological order using predictive models
• Super-resolving the Ising model with convolutional neural networks
• Machine Learning of Frustrated Classical Spin Models. II. Kernel Principal Component Analysis
• Prescribed Generative Adversarial Networks
• Divergence of predictive model output as indication of phase transitions
• Itinerant quantum critical point with frustration and non-Fermi-liquid
• Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks
• Variational autoencoder reconstruction of complex many-body physics
• Phase transition encoded in neural network
• A Review of Learning with Deep Generative Models from Perspective of Graphical Modeling
• Generation of ice states through deep reinforcement learning
• Effective Ruderman-Kittel-Kasuya-Yosida-like interaction in diluted double-exchange model: self-learning Monte Carlo approach
• Computing Absolute Free Energy with Deep Generative Models
• Phase space sampling and operator confidence with generative adversarial networks
• Implicit Autoencoders

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