Important progress has been made in micromagnetics, driven by its wide-ranging applications in magnetic storage design. Numerical simulation, a cornerstone of micromagnetics research, relies on first-principles rules to compute the dynamic evolution of micromagnetic systems using the renowned Landau–Lifshitz–Gilbert equation, named after Landau, Lifshitz and Gilbert. However, these simulations are often hindered by their slow speeds. Although fast Fourier transformation calculations reduce the computational complexity to O(Nlog(N)), it remains impractical for large-scale simulations. Here we introduce NeuralMAG, a deep learning approach to micromagnetic simulation. Our approach follows the Landau–Lifshitz–Gilbert iterative framework but accelerates computation of demagnetizing fields by employing a U-shaped neural network. This neural network architecture comprises an encoder that extracts aggregated spins at various scales and learns the local interaction at each scale, followed by a decoder that accumulates the local interactions at different scales to approximate the global convolution. This divide-and-accumulate scheme achieves a time complexity of O(N), notably enhancing the speed and feasibility of large-scale simulations. Unlike existing neural methods, NeuralMAG concentrates on the core computation—rather than an end-to-end approximation for a specific task—making it inherently generalizable. To validate the new approach, we trained a single model and evaluated it on two micromagnetics tasks with various sample sizes, shapes and material settings.

微磁学在磁性存储设计中的广泛应用推动了微磁学取得了重要进展。数值模拟是微磁学研究的基石，它依靠第一性原理规则，使用著名的 Landau-Lifshitz-Gilbert 方程（以 Landau、Lifshitz 和 Gilbert 命名）来计算微磁系统的动态演变。然而，这些模拟经常受到速度慢的阻碍。尽管快速傅里叶变换计算将计算复杂度降低到 O（Nlog（N）），但对于大规模仿真来说仍然不切实际。在这里，我们介绍了 NeuralMAG，这是一种用于微磁仿真的深度学习方法。我们的方法遵循 Landau-Lifshitz-Gilbert 迭代框架，但通过采用 U 形神经网络加速了退磁场的计算。这种神经网络架构包括一个编码器，该编码器提取各种尺度的聚合自旋并学习每个尺度的局部交互，然后是一个解码器，该解码器累积不同尺度的局部交互以近似全局卷积。这种除法累加方案实现了 O（N） 的时间复杂度，显著提高了大规模仿真的速度和可行性。与现有的神经方法不同，NeuralMAG 专注于核心计算，而不是特定任务的端到端近似，使其本质上是可推广的。为了验证新方法，我们训练了一个模型，并在具有不同样本大小、形状和材料设置的两个微磁任务上对其进行了评估。