Divergence of predictive model output as indication of phase transitions

Abstract

We introduce a new method to identify phase boundaries in physical systems. It is based on training a predictive model such as a neural network to infer a physical system's parameters from its state. The deviation of the inferred parameters from the underlying correct parameters will be most susceptible and diverge maximally in the vicinity of phase boundaries. Therefore, peaks in the divergence of the model's predictions are used as indication of phase transitions. Our method is applicable for phase diagrams of arbitrary parameter dimension and without prior information about the phases. Application to both the two-dimensional Ising model and the dissipative Kuramoto-Hopf model show promising results.

arXiv comment6 pages, 3 figures

References in corpus (24)

• Deep Learning in Neural Networks: An Overview
• Quantum Machine Learning
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• An introduction to quantum machine learning
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Collective dynamics in optomechanical arrays
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Reinforcement Learning in Different Phases of Quantum Control
• Active learning machine learns to create new quantum experiments
• Deep-learning Top Taggers or The End of QCD?
• Self-Learning Monte Carlo Method
• Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limit
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Reinforcement Learning with Neural Networks for Quantum Feedback
• Mutual Information, Neural Networks and the Renormalization Group
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Learning multiple order parameters with interpretable machines
• Learning phase transitions from dynamics
• Pattern phase diagram for 2D arrays of coupled limit-cycle oscillators

Cited by in corpus (27)

• Unsupervised machine learning and band topology
• Machine Learning for Quantum Matter
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Unsupervised identification of topological order using predictive models
• Unsupervised Learning of Non-Hermitian Topological Phases
• Analyzing non-equilibrium quantum states through snapshots with artificial neural networks
• Unsupervised learning using topological data augmentation
• Generative models for sampling and phase transition indication in spin systems
• Phase Detection with Neural Networks: Interpreting the Black Box
• Quantum kernels to learn the phases of quantum matter
• Interpretable and unsupervised phase classification
• Rapid Exploration of Topological Band Structures using Deep Learning
• Mott transition in a cavity-boson system: A quantitative comparison between theory and experiment
• Hessian-based toolbox for reliable and interpretable machine learning in physics
• Mapping out phase diagrams with generative classifiers
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Unsupervised identification of Floquet topological phase boundaries
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Adversarial Machine Learning Phases of Matter
• Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter
• Robust Identification of Topological Phase Transition by Self-Supervised Machine Learning Approach
• A learning algorithm with emergent scaling behavior for classifying phase transitions
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Machine learning the Ising transition: A comparison between discriminative and generative approaches
• Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems
• A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography