We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional $\mathrm{SU}(3)$ Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as $0.045$ fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions.

翻译：我们开发了一种基于非平衡模拟的方法论，以缓解在趋近格点规范理论的连续极限时出现的拓扑冻结问题。通过采用开放边界条件，我们降低了拓扑电荷的自相关性，同时利用非平衡蒙特卡洛方法逐步引入周期性边界条件，精确消除了其非物理效应。针对四维 $\mathrm{SU}(3)$ 杨-米尔斯理论，我们对该策略的计算成本进行了详细分析。在完全掌握其标度行为后，我们提出了一种在连续极限下高效采样拓扑的清晰策略，并在晶格间距小至 $0.045$ fm 的尺度上进行了验证。此外，我们通过设计一种定制化的随机归一化流来推广此方法，用于边界条件演化，获得了优于纯随机非平衡方法的性能，为未来更高效的基于流的解决方案奠定了基础。