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

TL;DR

This work tackles the challenge of generating physically consistent 3D coronal magnetic fields that evolve with the solar cycle. It introduces a denoising diffusion probabilistic model operating in the spherical-harmonic domain, leveraging the potential-field constraint $\mathbf{B}=-\nabla V$ with $\nabla^2 V=0$ to enforce $\nabla\cdot\mathbf{B}=0$. Trained on 11.7 years of ADAPT-WSA simulations with data augmentation, the model conditions on solar-cycle phase $S$ and yields samples that reproduce Heliospheric Current Sheet behavior appropriate to $S$ (e.g., near-equatorial configuration at solar minimum and more dynamic structure at solar maximum). The results indicate a viable pathway for physics-informed 3D generative modeling in Heliophysics with applications in solar forecasting, data assimilation, inverse problems, and physics-informed graphical asset generation.

Abstract

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.

Figures (4)

• Figure 1: Samples from the model with references example from the test set. Solar minimum is called such because the field lines are more structured, symmetric, and resemble a magnetic dipole. During solar maximum, the field lines are more chaotic and less like a dipole.
• Figure 2: Neural Architecture, utilizing time embedding, context, and skip connections.
• Figure 3: Illustration of the iterative reverse diffusion process for a $S=0$ sample.
• Figure 4: Plots of the Heliospheric Current Sheet (HCS) from random samples for $S=0$ and $S=1$.