Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations.

使用机器学习方法重新审视如何对固定点动作进行参数化，以获得四维SU(3)规范理论的固定点动作，从而获得优于以往研究的更好的参数化，这是未来蒙特卡洛模拟的必要第一步。

利用规范等变卷积神经网络对SU(3)规范理论的机器学习固定点行动