标题： 日冕中三维磁场的扩散建模 显示英文标题

标题： Diffusion Modeling of the Three-Dimensional Magnetic Field in the Sun's Corona

摘要： 在本工作中，我们引入了一种新颖的生成去噪扩散模型，用于合成太阳的三维日冕磁场，这是一个由不断演变的磁结构所表征的复杂且动态的区域。 尽管每天都有变化，这些结构表现出重复的模式和长期的周期性趋势，在物理与机器学习的交叉领域中带来了独特的建模挑战和机遇。 我们的生成方法采用了一种受球面傅里叶神经算子（SFNO）启发的创新架构，在球面谐波域中运行，其中标量场直接对应于在物理约束下的磁势。 我们使用了一个包含11.7年每日耦合模拟的广泛数据集对这个模型进行了训练，该数据集来自空军数据同化光球通量传输-王谢尔利阿尔杰（ADAPT-WSA）模型，并通过数据增强进行了进一步增强。 初步结果表明，该模型能够有条件地生成反映11年太阳周期内不同阶段的物理上现实的磁场：从太阳最小期（$S = 0$）到太阳最大期（$S = 1$）。 这种方法代表了在日地物理学中先进生成三维建模方面的重大进展，具有在太阳预报、数据同化、逆问题求解以及在程序生成物理信息图形资产等更广泛领域中的潜在应用。 显示英文摘要

摘要： In this work, we introduce a novel generative denoising diffusion model for synthesizing the Sun's three-dimensional coronal magnetic field, a complex and dynamic region characterized by evolving magnetic structures. Despite daily variability, these structures exhibit recurring patterns and long-term cyclic trends, presenting unique modeling challenges and opportunities at the intersection of physics and machine learning. Our generative approach employs an innovative architecture influenced by Spherical Fourier Neural Operators (SFNO), operating within the spherical harmonic domain, where the scalar field corresponds directly to the magnetic potential under physical constraints. We trained this model using an extensive dataset comprising 11.7 years of daily coupled simulations from the Air Force Data Assimilative Photospheric Flux Transport-Wang Sheeley Arge (ADAPT-WSA) model, further enhanced by data augmentation. Initial results demonstrate the model's capability to conditionally generate physically realistic magnetic fields reflective of distinct phases within the 11-year solar cycle: from solar minimum ($S = 0$) to solar maximum ($S = 1$). This approach represents a significant step toward advanced generative three-dimensional modeling in Heliophysics, with potential applications in solar forecasting, data assimilation, inverse problem-solving, and broader impacts in areas such as procedural generation of physically-informed graphical assets.