Utilizing Neural Networks for Solving Functional Renormalization Group Flow Equations
Abstract
A novel physics-informed neural networks (PINNs) based approach for solving functional renormalization group flow equations is presented. We investigate the finite temperature phase transition in O(N) models without relying on the large-N approximation, which was used in earlier attempts with similar methods. We argue that these previous solutions cannot easily be generalized for more complex symmetries, and hence our approach can provide new insight. Our technique relies on a series of ansätze that combines the small- and large-field approximation schemes with a neural network, leading to a highly accurate approximation over the entire field range. We compare the PINNs approach with traditional grid-based Runge-Kutta results and show that the network can successfully learn the temperature, field, and scale dependencies of the effective potential in the local potential approximation.
Related
- Quantum-Classical Neural Networks for Solving Lindblad Master Equations
- Quantum Complexity of Solving Linear Equations on Higher-Order Networks
- Gen-PINNs: Generative Adversarial Physics Informed Neural Networks for solving partial differential equations
- Nonperturbative functional renormalization group for Higgs-singlet models with physics-informed neural networks
- Multiloop functional renormalization group from single bosons
BibTeX
@misc{gurzo2026utilizing,
title = {{Utilizing Neural Networks for Solving Functional Renormalization Group Flow Equations}},
author = {J. Gurzó and G. Fejős},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13754},
eprint = {2610.13754},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13754},
}
RIS
TY - UNPB
TI - Utilizing Neural Networks for Solving Functional Renormalization Group Flow Equations
AU - J. Gurzó
AU - G. Fejős
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13754
UR - https://arxiv.org/abs/2610.13754
AB - A novel physics-informed neural networks (PINNs) based approach for solving functional renormalization group flow equations is presented. We investigate the finite temperature phase transition in O(N) models without relying on the large-N approximation, which was used in earlier attempts with similar methods. We argue that these previous solutions cannot easily be generalized for more complex symmetries, and hence our approach can provide new insight. Our technique relies on a series of ansätze that combines the small- and large-field approximation schemes with a neural network, leading to a highly accurate approximation over the entire field range. We compare the PINNs approach with traditional grid-based Runge-Kutta results and show that the network can successfully learn the temperature, field, and scale dependencies of the effective potential in the local potential approximation.
ER -