A cautionary tale for machine learning generated configurations in presence of a conserved quantity

2020/07/19 by Ahmadreza Azizi, Michel Pleimling
Materials Science · Physics and Astronomy · #Artificial neural network #Boltzmann machine #Convolutional neural network #Energy (signal processing) #Ising model #Machine Learning in Materials Science #Monte Carlo method #Point (geometry) #Quantum many-body systems #Restricted Boltzmann machine #Scaling #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1038/s41598-021-85683-8

published as Scientific Reports 11, 6395 (2021) · 21 pages, 9 figures, submitted for publication to the Physical Review E

arxiv created 2020/07/19 · openalex created_date 2020/07/23 · openalex publication_date 2021/03/18 · arxiv updated 2021/03/19 · openalex updated_date 2026/08/06

Abstract

We investigate the performance of machine learning algorithms trained exclusively with configurations obtained from importance sampling Monte Carlo simulations of the two-dimensional Ising model with conserved magnetization. For supervised machine learning, we use convolutional neural networks and find that the corresponding output not only allows to locate the phase transition point with high precision, it also displays a finite-size scaling characterized by an Ising critical exponent. For unsupervised learning, restricted Boltzmann machines (RBM) are trained to generate new configurations that are then used to compute various quantities. We find that RBM generates configurations with magnetizations and energies forbidden in the original physical system. The RBM generated configurations result in energy density probability distributions with incorrect weights as well as in wrong spatial correlations. We show that shortcomings are also encountered when training RBM with configurations obtained from the non-conserved Ising model.

Citations

• A Practical Guide to Training Restricted Boltzmann Machines
• Predicting Crystal Structures with Data Mining of Quantum Calculations
• Training Products of Experts by Minimizing Contrastive Divergence
• Face recognition: a convolutional neural-network approach
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning quantum phases of matter beyond the fermion sign problem
• Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders
• Scale-invariant feature extraction of neural network and renormalization group flow
• Machine learning of phase transitions in the percolation andXYmodels
• Applications of neural networks to the studies of phase transitions of two-dimensional Potts models
• Restricted Boltzmann machines in quantum physics
• Machine-Learning Studies on Spin Models