2019/12/19 by Jui-Hui Chung, Chung, Jui-Hui, Ying-Jer Kao +1
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Artificial neural network #Boltzmann machine #Computer science #Critical exponent #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Distribution (mathematics) #Divergence (linguistics) #Exponent #FOS: Physical sciences #Geometry #Group (periodic table) #Ising model #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Space (punctuation) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Theoretical and Computational Physics #Transformation (genetics) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1912.09005
published in arXiv (Cornell University) (Cornell University) · Published as a proceeding of Workshop on Machine Learning and the Physical Sciences at the 33rd Conference on Neural Information Processing Systems (NeurIPS) https://ml4physicalsciences.github.io/
arxiv created 2019/12/19 · openalex publication_date 2019/12/19 · arxiv updated 2019/12/20 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system. The scheme is based on minimizing the Kullback-Leibler divergence between the distribution of the system and the normalized normalizing factor of the transformation parametrized by a restricted Boltzmann machine. We compute the thermal critical exponent of the two-dimensional Ising model using the trained optimal projector and obtain a very accurate thermal critical exponent yt=1.0001(11) after the first step of the transformation.