Topological magnetic textures observed in experiments can, in principle, be predicted by theoretical calculations and numerical simulations. However, such calculations are, in general, hampered by difficulties in distinguishing between local and global energy minima. This becomes particularly problematic for magnetic materials that allow for a multitude of topological charges. Finding solutions to such problems by means of classical numerical methods can be challenging because either a good initial guess or a gigantic amount of random sampling is required. In this study, we demonstrate an efficient way to identify those metastable configurations by leveraging the power of gradient descent-based optimization within the framework of a feedforward neural network combined with a heuristic meta-search, which is driven by a random perturbation of the neural network's input. We exemplify the power of the method by an analysis of the Pd/Fe/Ir(111) system, an experimentally well characterized system.

翻译：实验观测到的拓扑磁结构在理论上可以通过理论计算和数值模拟预测。然而，这类计算通常因难以区分局域能量极小值与全局能量极小值而受阻。对于允许存在多种拓扑电荷数的磁性材料来说，这一问题尤为突出。通过经典数值方法求解此类问题颇具挑战性，因为要么需要良好的初始猜测，要么需要进行海量随机采样。在本研究中，我们展示了一种高效识别这些亚稳态构型的方法：该方法在前馈神经网络框架内结合梯度下降优化的能力，并引入由神经网络输入的随机扰动驱动的启发式元搜索。我们通过分析实验表征完善的Pd/Fe/Ir(111)体系，展示了该方法的强大功能。