Thermodynamics and feature extraction by machine learning

2018/10/18 by Shotaro Shiba, Shotaro Shiba Funai, Dimitrios Giataganas
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Computer science #Condensed matter physics #Critical exponent #Critical point (mathematics) #Criticality #Ising model #Machine Learning in Materials Science #Mathematical analysis #Mathematics #Observable #Phase transition #Physical system #Physics #Quantum many-body systems #Quantum mechanics #Renormalization group #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #cs.LG #hep-th

paper · pdf · doi:10.1103/physrevresearch.2.033415

published as Phys. Rev. Research 2, 033415 (2020) · 11 pages, double column format, 10 figures

arxiv created 2018/10/18 · openalex publication_date 2020/09/15 · arxiv updated 2020/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a restricted Boltzmann machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near-criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the renormalization group (RG) flow of the lattice model. Our results suggest an explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated with the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.

Citations

• Machine learning for many-body physics: efficient solution of dynamical mean-field theory
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Training Products of Experts by Minimizing Contrastive Divergence
• Learning multiple layers of representation
• Searching for exotic particles in high-energy physics with deep learning
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Why does deep and cheap learning work so well?
• Machine learning quantum phases of matter beyond the fermion sign problem
• Restricted Boltzmann machines for the long range Ising models
• Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders
• Scale-invariant feature extraction of neural network and renormalization group flow
• Deep learning and the AdS/CFT correspondence
• A high-bias, low-variance introduction to Machine Learning for physicists
• Deep learning