Physics-informed neural networks for solving functional renormalization group on a lattice

Addressing high-dimensional partial differential equations 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 physics-informed neural networks (PINNs) as a state-of-the-art machine-learning method for solving high-dimensional partial differential equations to overcome this challenge. In a zero-dimensional $\mathrm{O}(N)$ model, we numerically demonstrate the construction of an effective action on an $N$-dimensional 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.