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Inverse renormalization group based on image super-resolution using deep convolutional networks.

Kenta Shiina1,2, Hiroyuki Mori3, Yusuke Tomita4

  • 1Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397, Japan. 16879316kenta@gmail.com.

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This study explores the inverse renormalization group using deep learning for image super-resolution. Improved correlation configurations and block-cluster transformations successfully reproduce original models, enabling finite-size scaling in enlarged systems.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Machine Learning

Background:

  • Renormalization group methods are crucial for understanding critical phenomena in statistical physics.
  • Traditional methods often rely on spin configurations, which can be computationally intensive.
  • Image super-resolution techniques offer novel approaches to data augmentation and analysis.

Purpose of the Study:

  • To investigate the inverse renormalization group using deep convolutional neural networks for image super-resolution.
  • To explore the efficacy of improved correlation configurations over traditional spin configurations.
  • To adapt block-cluster transformations for enhanced estimators in Monte Carlo simulations.

Main Methods:

  • Utilizing deep convolutional neural networks for image super-resolution.
  • Applying improved correlation configurations instead of spin configurations for 2D Ising and three-state Potts models.
  • Implementing a block-cluster transformation as an alternative to block-spin transformation within a dual Monte Carlo algorithm framework.
  • Employing an enlargement rule for repeated inverse renormalization procedures.

Main Results:

  • The super-resolution scheme successfully reproduced original configurations using renormalized improved correlation configurations across all temperatures.
  • The block-cluster transformation was shown to operate on graph degrees of freedom, distinct from the spin degrees of freedom of block-spin transformations.
  • Generated enlarged systems using super-resolution adhered to finite-size scaling principles.
  • An approximate temperature rescaling was discussed to link enlarged systems to thermodynamics.

Conclusions:

  • Deep learning-based super-resolution provides a viable method for inverse renormalization group studies.
  • Improved correlation configurations and block-cluster transformations offer effective alternatives for analyzing spin models.
  • The developed framework successfully generates larger systems that satisfy finite-size scaling, bridging statistical mechanics and machine learning.