Generative Simulations of The Solar Corona Evolution With Denoising Diffusion : Proof of Concept

TL;DR

This work demonstrates that generative deep learning methods, such as Denoising Diffusion Probabilistic Models (DDPM), can be successfully applied to simulate future evolutions of the corona as observed in Extreme Ultraviolet (EUV) wavelengths.

Abstract

The solar magnetized corona is responsible for various manifestations with a space weather impact, such as flares, coronal mass ejections (CMEs) and, naturally, the solar wind. Modeling the corona's dynamics and evolution is therefore critical for improving our ability to predict space weather In this work, we demonstrate that generative deep learning methods, such as Denoising Diffusion Probabilistic Models (DDPM), can be successfully applied to simulate future evolutions of the corona as observed in Extreme Ultraviolet (EUV) wavelengths. Our model takes a 12-hour video of an Active Region (AR) as input and simulate the potential evolution of the AR over the subsequent 12 hours, with a time-resolution of two hours. We propose a light UNet backbone architecture adapted to our problem by adding 1D temporal convolutions after each classical 2D spatial ones, and spatio-temporal attention in the bottleneck part. The model not only produce visually realistic outputs but also captures the inherent stochasticity of the system's evolution. Notably, the simulations enable the generation of reliable confidence intervals for key predictive metrics such as the EUV peak flux and fluence of the ARs, paving the way for probabilistic and interpretable space weather forecasting. Future studies will focus on shorter forecasting horizons with increased spatial and temporal resolution, aiming at reducing the uncertainty of the simulations and providing practical applications for space weather forecasting. The code used for this study is available at the following link: https://github.com/gfrancisco20/video_diffusion

Figures (4)

• Figure 1: Reliability diagrams. The X-axis represents the Confidence Intervals (CIs) derived from the simulations. The left Y-axis represents the frequency at which actual observations fall into the derived CIs, corresponding to the blue curve. The red bars represent the size of the CIs, expressed as a percentage of the observed value for fluence and MPF, with one tile on the Y-axis grid representing 20% uncertainty. For the T2PF, the red bar scale (right Y-axis) is in hours, with each tile representing 2H of uncertainty. A perfectly reliable model has a blue curve aligned with the diagonal and provides minimal uncertainty for a given confidence interval, represented by smaller red bars.
• Figure 2: Predictions for AR 8195 on 2022-05-04 at 20:00. The AR exhibited a series of numerous C-class and M-class flares during the 12 hours prior to the prediction time, as well as during subsequent 12 hours. Remnants of these flares can be observed as brightenings in the frames, both in the first row (previous 12 hours) and in the second row (next 12 hours ground truth). Similar brightening can be observed in the three simulation results exhibited from the third to fifth row. The sixth row presents the pixel-wise percentage deviation from the ground truth, averaged over 20 simulations. The final row displays standard deviation maps computed over the same 20 simulations. Animations links : https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/8195_20220504_2000_simu_0.gif, https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/8195_20220504_2000_simu_1.gif, https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/8195_20220504_2000_simu_2.gif.
• Figure 3: Predictions for AR 8977 on 2023-01-18 at 06:00. The -6H input frame shows the remnants of an M1.8 flare that occurred approximately 6.5 hours prior to the time of prediction. In the +6H ground truth frame, which represents the forecasted target, we observe the remnants of another M1.8 flare that concluded on 2023-01-18 at 10:52. A similar brightening is visible in the +6H frame of Simulation 0. The mean percentage pixel-wise error, averaged over 20 simulations, indicates that errors are larger during this event. The standard deviation map shows the pixel-wise standard deviation across 20 simulations, providing insight into the areas where the model is most uncertain. This highlights regions at higher risk for extreme events, such as the flare remnants seen in the +6H frame. Animations links : https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/8977_20230118_0600_simu_0.gif, https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/8977_20230118_0600_simu_1.gif, https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/8977_20230118_0600_simu_2.gif.
• Figure 4: Predictions for AR 9188 on 2023-03-08 at 22:00. The AR exhibited a series of C-class and M-class flares during the [-10H, +12H] time window around the forecasting time. The -10H input frame shows strong remnants of a C flare that ended 30 minutes before the frame's timestamp. The +2H ground truth frame displays the fading remnants of an M1.3 flare, which ended about 1 hour and 10 minutes earlier. The +12H frame exhibits strong remnants of a C3.1 flare ending 40 minutes before. Simulations 0 and 1 display a similar brightening in the +10H frame, while Simulation 2 shows one in the +6H frame. The mean percentage error indicates that overall activity is mostly underestimated, particularly around the upper loop where the M-class flare occurred, showing difficulty in predicting this flare and its aftermath. The standard deviation map shows increased uncertainty in the lower part of the sigmoid, where the C3.1 flare occurs between the +10H and +12H frames, suggesting that the model forecasted the possibility of similar events between the +6H and +12H frames, where the standard deviations are higher. Animations links : https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/9188_20230308_2200_simu_0.gif, https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/9188_20230308_2200_simu_1.gif, https://github.com/gfrancisco20/video_diffusion/blob/master/paper_simulations/9188_20230308_2200_simu_2.gif.