Speaker
Description
Although the formulation of the FRG is exact, practical calculations must be carried out approximately. This is because solvers for functional differential equations (FDEs), such as the Wetterich equation, have not yet been established. Meanwhile, physics-informed neural networks (PINNs) have recently gained attention as an efficient method for solving high-dimensional partial differential equations. Since FDEs are essentially high-dimensional differential equations, PINNs are expected to serve as useful solvers for the FRG. In this talk, I will discuss the application of PINNs to the FRG. In particular, I will present numerical applications to low-dimensional scalar models to demonstrate their applicability. In our approach, the effective action is represented by a neural network, and I will discuss network architectures that help ensure convexity, which is important for describing phase transitions. This talk is based on Refs. [1,2].
[1] T. Yokota, Physics-informed neural networks for solving functional renormalization group on a lattice, Phys. Rev. B 109, 214205 (2024).
[2] T. Miyagawa and T. Yokota, Physics-informed neural networks for functional differential equations: cylindrical approximation and its convergence guarantees, NeurIPS2024 (2024).
| Affiliation | Osaka Institute of Technology |
|---|---|
| Link to paper | https://doi.org/10.1103/PhysRevB.109.214205, https://doi.org/10.48550/arXiv.2410.18153 |
| Career status | Senior |