NeuralMAG: Fast and Generalizable Micromagnetic Simulation with Deep Neural Nets

These authors contributed equally to this work. Abstract Micromagnetics has made significant strides, particularly due to its wide-ranging applications in magnetic storage design and the recent exciting advancements in spintronics research. Numerical simulation is a cornerstone of micromagnetics research, relying on first-principle rules to compute the dynamic evolution of micromagnetic systems based on the renowned LLG equation, named after Landau, Lifshitz, and Gilbert. However, simulations are often hindered by their slow speed, primarily due to the global convolution required to compute the demagnetizing field, which involves full interaction among any two units in the sample. Although Fast-Fourier transformation (FFT) calculations reduce the computational complexity to O(NlogN), it remains impractical for large-scale simulations. In this paper, we introduce NeuralMAG, a deep learning approach to micromagnetic simulation. Our innovative approach follows the LLG iterative framework but accelerates demagnetizing field computation through the employment of a U-shaped neural network (Unet). The Unet 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), significantly enhancing the speed and feasibility of large-scale simulations. 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: (1) basic LLG dynamic evolution, and (2) MH curve estimation. The results show that the model maintains reasonable accuracy and is significantly faster than the conventional FFT-based method, achieving a sixfold speedup for large-size models. NeuralMAG has been published online and is available for users to download. Born in the early 20th century to address the issues of magnetic domain and hysteresis, micromagnetics has evolved into the fundamental methodology for understanding the magnetic behavior of materials from a microscopic view [1, 2].