Physics-informed neural network for solving functional renormalization group on lattice

Author:

Takeru Yokota

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el), High Energy Physics - Lattice (hep-lat), High Energy Physics - Theory (hep-th)

journal:

RIKEN-iTHEMS-Report-23

date:

2023-12-26 00:00:00

Abstract

Addressing high-dimensional partial differential equations (HDPDEs) to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even on lattices. We leverage a physics-informed neural network (PINN) as a state-of-the-art machine learning method for solving HDPDEs to overcome this challenge. In a 0-D O($N$) model, we numerically demonstrate the construction of an effective action on an $N$-D configuration space, extending up to $N=100$. Our results underscore the effectiveness of PINN approximation, even in scenarios lacking small parameters such as a small coupling.

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