Magnetic Field Evolution of the Solar Active Region 13664

On 2024 May 10-11, the strongest geomagnetic storm since 2003 November occurred, with a peak Dst index of -412 nT. The storm was caused by NOAA active region (AR) 13664, which was the source of a large number of coronal mass ejections and flares, including 12 X-class flares. Starting from about May 7, AR 13664 showed a steep increase in its size and (free) magnetic energy, along with increased flare activity. In this study, we perform 3D magnetic field extrapolations with the NF2 nonlinear force-free code based on physics-informed neural networks (R. Jarolim et al.). In addition, we introduce the computation of the vector potential to achieve divergence-free solutions. We extrapolate vector magnetograms from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager at the full 12 minute cadence from 2024 May 5 00:00 to 11 04:36 UT, in order to understand the AR's magnetic evolution and the large eruptions it produced. A decrease in the calculated relative free magnetic energy can be related to solar flares in similar to 90% of the cases, and all considered X-class flares are reflected by a decrease in the relative free magnetic energy. Regions of enhanced free magnetic energy and depleted magnetic energy between the start and end times of major X-class flares show spatial alignment with brightness increases in extreme-ultraviolet observations. We provide a detailed analysis of the X3.9-class flare on May 10, where we show that the interaction between separated magnetic domains is directly linked to major flaring events. With this study, we provide a comprehensive data set of the magnetic evolution of AR 13664 and make it publicly available for further analysis.