Renormalization-guided inverse blocking for lattice field generation: construction and validation
Abstract
We propose an algorithm for generating lattice field configurations based on the approximate inversion of a renormalization-group blocking transformation. We optimize the blocking transformation using a ``perfect blocking'' condition so that the blocked lattice distribution is well approximated by a simple coarse action. The blocking is separated into an invertible smoothing transformation followed by decimation. Machine learning, in the form of a conditional normalizing flow, is used to reconstruct the short-distance degrees of freedom removed by the decimation. A short fine-action rethermalization then removes the residual mismatch. Because the coarse ensemble supplies the long-distance modes, the same blocking transformation and conditional flow can be reused recursively on larger lattices, producing a cascade of configurations from an initial small-volume ensemble. We test the method in two-dimensional ϕ4 theory with λ=1 at criticality and demonstrate stable cascade upscaling from 162 to 20482 lattices on local computational resources. Controlled rethermalization tests show that short-distance mismatches relax rapidly, whereas a deliberately introduced mismatch in the relevant thermal direction relaxes much more slowly. The construction uses ingredients that admit natural extensions to higher-dimensional systems and, ultimately, to gauge and fermionic degrees of freedom.
Related
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BibTeX
@misc{hasenfratz2026renormalizationguided,
title = {{Renormalization-guided inverse blocking for lattice field generation: construction and validation}},
author = {Anna Hasenfratz and Ethan T. Neil and Letizia Parato and Noah Schwartz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.28580},
eprint = {2608.28580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28580},
}
RIS
TY - UNPB
TI - Renormalization-guided inverse blocking for lattice field generation: construction and validation
AU - Anna Hasenfratz
AU - Ethan T. Neil
AU - Letizia Parato
AU - Noah Schwartz
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.28580
UR - https://arxiv.org/abs/2608.28580
AB - We propose an algorithm for generating lattice field configurations based on the approximate inversion of a renormalization-group blocking transformation. We optimize the blocking transformation using a ``perfect blocking'' condition so that the blocked lattice distribution is well approximated by a simple coarse action. The blocking is separated into an invertible smoothing transformation followed by decimation. Machine learning, in the form of a conditional normalizing flow, is used to reconstruct the short-distance degrees of freedom removed by the decimation. A short fine-action rethermalization then removes the residual mismatch. Because the coarse ensemble supplies the long-distance modes, the same blocking transformation and conditional flow can be reused recursively on larger lattices, producing a cascade of configurations from an initial small-volume ensemble. We test the method in two-dimensional ϕ^4 theory with λ=1 at criticality and demonstrate stable cascade upscaling from 16^2 to 2048^2 lattices on local computational resources. Controlled rethermalization tests show that short-distance mismatches relax rapidly, whereas a deliberately introduced mismatch in the relevant thermal direction relaxes much more slowly. The construction uses ingredients that admit natural extensions to higher-dimensional systems and, ultimately, to gauge and fermionic degrees of freedom.
ER -