Nonperturbative functional renormalization group for Higgs-singlet models with physics-informed neural networks
Abstract
We develop a nonperturbative functional renormalization group framework within the LPA' to solve the Wetterich flow equation for the Z2-symmetric real singlet extension of the Standard Model at finite temperature, without a low-order polynomial truncation of the loop corrections to the effective potential, using a physics-informed neural network (PINN) representation. In contrast to conventional truncations based on low-order field expansions, our hybrid tree-level-plus-neural-network ansatz yields a continuous, mesh-free description of the effective potential over the full field and scale range. As a proof of concept, we apply the framework to the finite-temperature effective potential relevant to the electroweak phase transition: one-dimensional field-space slices at two benchmark temperatures, and a two-dimensional reconstruction at T=100 GeV yielding a two-step bounce action. The flow is implemented in a multi-domain setup in scale and field space with derivative matching conditions ensuring smoothness and numerical stability. Gauge and Yukawa sectors are incorporated via independently computed perturbative two-loop running couplings, and anomalous dimensions are included in the flow at the LPA' level. We benchmark the network against resummed perturbation theory and against a grid-based relaxation solver of the same equation. Finally, we introduce a soft consistency constraint that keeps the solution close, in sign and order of magnitude, to perturbation theory across the field-space domain. We find this constraint necessary, rather than merely helpful, for selecting a physically sensible solution of the flow equation. The converged result nevertheless retains a residual dependence on this guidance -- through hand-tuned weights and an analytic thermal target -- which we identify as the central open problem for mesh-free FRG treatments of this kind.
Related
- Utilizing Neural Networks for Solving Functional Renormalization Group Flow Equations
- Multiloop functional renormalization group from single bosons
- Scaling and Renormalization in Neural Networks: An Effective Renormalization-Group Description of Grokking
- Multiscale Renormalization of Weighted Networks
- Functional renormalization group in an external field: constant field versus constant order parameter
BibTeX
@misc{yokozaki2026nonperturbative,
title = {{Nonperturbative functional renormalization group for Higgs-singlet models with physics-informed neural networks}},
author = {Norimi Yokozaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08470},
eprint = {2609.08470},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08470},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonperturbative functional renormalization group for Higgs-singlet models with physics-informed neural networks
AU - Norimi Yokozaki
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.08470
UR - https://arxiv.org/abs/2609.08470
AB - We develop a nonperturbative functional renormalization group framework within the LPA' to solve the Wetterich flow equation for the Z_2-symmetric real singlet extension of the Standard Model at finite temperature, without a low-order polynomial truncation of the loop corrections to the effective potential, using a physics-informed neural network (PINN) representation. In contrast to conventional truncations based on low-order field expansions, our hybrid tree-level-plus-neural-network ansatz yields a continuous, mesh-free description of the effective potential over the full field and scale range. As a proof of concept, we apply the framework to the finite-temperature effective potential relevant to the electroweak phase transition: one-dimensional field-space slices at two benchmark temperatures, and a two-dimensional reconstruction at T=100 GeV yielding a two-step bounce action. The flow is implemented in a multi-domain setup in scale and field space with derivative matching conditions ensuring smoothness and numerical stability. Gauge and Yukawa sectors are incorporated via independently computed perturbative two-loop running couplings, and anomalous dimensions are included in the flow at the LPA' level. We benchmark the network against resummed perturbation theory and against a grid-based relaxation solver of the same equation. Finally, we introduce a soft consistency constraint that keeps the solution close, in sign and order of magnitude, to perturbation theory across the field-space domain. We find this constraint necessary, rather than merely helpful, for selecting a physically sensible solution of the flow equation. The converged result nevertheless retains a residual dependence on this guidance -- through hand-tuned weights and an analytic thermal target -- which we identify as the central open problem for mesh-free FRG treatments of this kind.
ER -