Generating configurations of increasing lattice size with machine learning and the inverse renormalization group

Aug 5, 2026

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The work reviews recent machine-learning approaches to inverse renormalization group (IRG) methods, originally introduced as generative numerical techniques via compatible Monte Carlo simulations. IRG enables iterative generation of lattice configurations at larger sizes while avoiding critical slowing down. The discussion covers constructing IRG transformations with convolutional neural networks, and applies these ideas to statistical mechanics, lattice field theory, and disordered systems, emphasizing the three-dimensional Edwards–Anderson spin glass for volumes beyond current supercomputer access.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Inverse Monte Carlo renormalization group

Kernel construction via machine learning

Inverse renormalization group of quantum field theories

Real-space transformations for the Φ4 model

Brower-Tamayo simulation setup

arXiv :2405 . 16288v1 [hep-lat] 25 May 2024 Generating configurations of increasing lattice size with machine learning and the inverse renormalization group Dimitrios Bachtis􀀰,∗ 􀀰 Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France E-mail: [dimitrios.bachtis@phys.ens.fr](dimitrios.bachtis@phys.ens.fr) We review recent developments of machine learning algorithms pertinent to the inverse renormalization group, which was originally established as a generative numerical method by RonSwendsen-Brandt via the implementation of compatible Monte Carlo simulations. Inverse renormalization group methods enable the iterative generation of configurations for increasing lattice size without the critical slowing down effect. We discuss the construction of inverse renormalization group transformations with the use of convolutional neural networks and present applications in models of statistical mechanics, lattice field theory, and disordered systems. We highlight the case of the three-dimensional Edwards-Anderson spin glass, where the inverse renormalization group can be employed to construct configurations for lattice volumes that have not yet been accessed by dedicated supercomputers. European network for Particle physics, Lattice field theory and Extreme computing (EuroPLEx2023) 11-15 September 2023 Berlin, Germany ∗ Speaker © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4 .0 International License (CC BY-NC-ND 4 .0) . [https://pos.sissa.it/](https://pos.sissa.it/) 1. Inverse Monte Carlo renormalization group Inverse renormalization group methods were originally established as generative numerical techniques by Ron-Swendsen-Brandt via the implementation of compatible Monte Carlo simulations [1] . The authors implemented the method on configurations of the three-dimensional Ising model with lattice volume 􀀫 = 43 to construct inversely renormalized systems up to lattices of 􀀫 = 1283. The discussed approach relies on the implementation of a Monte Carlo technique to ensure a computationally stable inverse transformation, is shown to evade the critical slowing down effect for the case of the three-dimensional Ising model, and provides accurate calculations of the critical exponents. Machine learning algorithms have recently revolutionized multiple aspects of academia and industry, and a natural question is whether neural networks could be employed to confront the mathematically ill-defined problem of constructing inverse renormalization group transformations. A straightforward approach would then consider the application of a standard real-space transformation with a rescaling factor of 􀀱, such as the majority rule, on original configurations of a given lattice size 􀀡 to construct renormalized configurations of lattice size 􀀡′ = 􀀡/􀀱 . One could then present the renormalized configurations of 􀀡′ as input to a machine learning algorithm, such as a set of (transposed) convolutions, in order to approximately reproduce the original configurations of size 􀀡 . This implementation then defines the construction of a kernel for an inverse transformation which can be arbitrarily optimized to approximate the inversion of a standard renormalization group transformation, such as the majority rule, by increasing the set of variational parameters, namely the weights and biases of the machine learning algorithm. The benefit of the discussed approach is that if one considers only a set of convolutions in the machine learning implementation, which can be applied irrespective of the lattice size, one could then increase the volume of the system for an arbitrary number of times via consecutive applications of the inverse transformation. Inverse renormalization group transformations have been constructed with a variety of machine learning architectures, including convolutional

FAQs

What problem does the inverse renormalization group (IRG) address for lattice simulations?

IRG provides an iterative way to generate configurations for increasing lattice sizes without the critical slowing down that typically hampers direct Monte Carlo scaling.

How do machine learning algorithms contribute to constructing inverse renormalization transformations?

The approach uses neural networks—such as convolutional neural networks—to build a trainable kernel that approximately inverts a standard renormalization group transformation by optimizing weights and biases.

Why is the three-dimensional Edwards–Anderson spin glass highlighted?

IRG can be used to construct lattice configurations for larger volumes that have not yet been reached by dedicated supercomputers.

Aug 5, 2026

Upload by Levi