Parameter Optimization of Domain-Wall Fermion using Machine Learning

Abstract

We study a parameter optimization of domain-wall fermions to improve chiral symmetry based on machine learning. Domain-wall fermions involve coefficients along the fifth dimension, which can be treated as trainable parameters to reduce the chiral symmetry violation caused by the finite extent of the fifth dimension. As the loss function, we use the residual mass estimated stochastically on a single gauge configuration. Numerical tests on a $L^3\times T\times L_5=4^3\times8\times8$ lattice demonstrate the feasibility of this framework.

Figures (3)

• Figure 1: Training history of the loss function for the Möbius and general settings.
• Figure 2: Training history of the Möbius parameters $b$ and $c$.
• Figure 3: Training histories of the slice-dependent domain-wall parameters $b_s$ (left) and $c_s$ (right) in the general setting.