Normally, these models work by inverting the process of natural diffusion, where they start with a distribution of random noise and progressively transform it into a structured data distribution resembling the training data. This transformation occurs in multiple steps, which incrementally denoise the noisy sample until it reaches the desired complexity and detail. In contrast to the normal diffusion models mentioned above (Song et al. 2022, 2024), which generate synthetic images by denoising random noise distributions without incorporating any specific guidance, our GenMDI model generates a synthetic image considering the previous image and the next image surrounding the generated image. This image generation process with guidance or condition is known as the conditional diffusion process, which is often used in the generation of video frames (Voleti et al. 2022). By conditioning the reverse diffusion process on the previous and subsequent images, GenMDI ensures that the generated image maintains continuity and reflects the dynamics of the surrounding images. This approach not only preserves the natural flow and consistency of MDI time-series magnetograms but also enhances our model's ability to accurately generate synthetic images. To our knowledge, this is the first time a conditional diffusion model has been used to improve the temporal resolution of MDI magnetograms. The remainder of this paper is organized as follows. Section 2 describes the data used in this study.

We present a transformer model, named DeepHalo, to predict the occurrence of halo coronal mass ejections (CMEs). Our model takes as input an active region (AR) and a profile, where the profile contains a time series of data samples in the AR that are collected 24 hours before the beginning of a day, and predicts whether the AR would produce a halo CME during that day. Each data sample contains physical parameters, or features, derived from photospheric vector magnetic field data taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). We survey and match CME events in the Space Weather Database Of Notification, Knowledge, Information (DONKI) and Large Angle and Spectrometric Coronagraph (LASCO) CME Catalog, and compile a list of CMEs including halo CMEs and non-halo CMEs associated with ARs in the period between November 2010 and August 2023. We use the information gathered above to build the labels (positive versus negative) of the data samples and profiles at hand, where the labels are needed for machine learning. Experimental results show that DeepHalo with a true skill statistics (TSS) score of 0.907 outperforms a closely related long short-term memory network with a TSS score of 0.821. To our knowledge, this is the first time that the transformer model has been used for halo CME prediction.

Solar flares are defined as outbursts on the surface of the Sun. They occur when energy accumulated in magnetic fields enclosing solar active regions (ARs) is abruptly expelled. Solar flares and associated coronal mass ejections are sources of space weather that adversely impact devices at or near Earth, including the obstruction of high-frequency radio waves utilized for communication and the deterioration of power grid operations. Tracking and delivering early and precise predictions of solar flares is essential for readiness and catastrophe risk mitigation. This paper employs the random forest (RF) model to address the binary classification task, analyzing the links between solar flares and their originating ARs with observational data gathered from 2011 to 2021 by SolarMonitor.org and the XRT flare database. We seek to identify the physical features of a source AR that significantly influence its potential to trigger >=C-class flares. We found that the features of AR_Type_Today, Hale_Class_Yesterday are the most and the least prepotent features, respectively. NoS_Difference has a remarkable effect in decision-making in both global and local interpretations.

The application of machine learning to the study of coronal mass ejections (CMEs) and their impacts on Earth has seen significant growth recently. Understanding and forecasting CME geoeffectiveness is crucial for protecting infrastructure in space and ensuring the resilience of technological systems on Earth. Here we present GeoCME, a deep-learning framework designed to predict, deterministically or probabilistically, whether a CME event that arrives at Earth will cause a geomagnetic storm. A geomagnetic storm is defined as a disturbance of the Earth's magnetosphere during which the minimum Dst index value is less than -50 nT. GeoCME is trained on observations from the instruments including LASCO C2, EIT and MDI on board the Solar and Heliospheric Observatory (SOHO), focusing on a dataset that includes 136 halo/partial halo CMEs in Solar Cycle 23. Using ensemble and transfer learning techniques, GeoCME is capable of extracting features hidden in the SOHO observations and making predictions based on the learned features. Our experimental results demonstrate the good performance of GeoCME, achieving a Matthew's correlation coefficient of 0.807 and a true skill statistics score of 0.714 when the tool is used as a deterministic prediction model. When the tool is used as a probabilistic forecasting model, it achieves a Brier score of 0.094 and a Brier skill score of 0.493. These results are promising, showing that the proposed GeoCME can help enhance our understanding of CME-triggered solar-terrestrial interactions.

Studying the sun's outer atmosphere is challenging due to its complex magnetic fields impacting solar activities. Magnetohydrodynamics (MHD) simulations help model these interactions but are extremely time-consuming (usually on a scale of days). Our research applies the Fourier Neural Operator (FNO) to accelerate the coronal magnetic field modeling, specifically, the Bifrost MHD model. We apply Tensorized FNO (TFNO) to generate solutions from partial differential equations (PDEs) over a 3D domain efficiently. TFNO's performance is compared with other deep learning methods, highlighting its accuracy and scalability. Physics analysis confirms that TFNO is reliable and capable of accelerating MHD simulations with high precision. This advancement improves efficiency in data handling, enhances predictive capabilities, and provides a better understanding of magnetic topologies.

Deep learning, which is a subfield of machine learning, has drawn significant interest in recent years. It was originally used in speech recognition (Deng, Hinton, and Kingsbury, 2013), natural language processing (Kastrati et al., 2021), and computer vision (Hu et al., 2018). More recently, it has been applied to astronomy, astrophysics, and solar physics (Liu et al., 2020a; Jiang et al., 2021; Espuña Fontcuberta et al., 2023; Mercea et al., 2023; Scully et al., 2023). Here, we present a new deep-learning method, specifically an attention-aided convolutional neural network (CNN), named SolarCNN, for solar image super-resolution. SolarCNN aims to enhance the quality of line-of-sight (LOS) magnetograms of solar active regions (ARs) collected by the Michelson Doppler Imager (MDI; Scherrer et al., 1995) on board the Solar and Heliospheric Observatory (SOHO; Domingo, Fleck, and Poland, 1995). The ground-truth labels used for training SolarCNN are the LOS magnetograms of the same ARs collected by the Helioseismic and Magnetic Imager (HMI; Schou et al., 2012) on board the Solar Dynamics Observatory (SDO; Pesnell, Thompson, and Chamberlin, 2012). Training and test samples are collected from ARs in the HMI and MDI overlap period, between 1 May 2010 and 11 April 2011. An AR on the solar disk usually consists of one or more sunspots and pores that are formed because of the concentrations of strong magnetic fields.

Model compression is a crucial part of deploying neural networks (NNs), especially when the memory and storage of computing devices are limited in many applications. This paper focuses on two model compression techniques: low-rank approximation and weight pruning in neural networks, which are very popular nowadays. However, training NN with low-rank approximation and weight pruning always suffers significant accuracy loss and convergence issues. In this paper, a holistic framework is proposed for model compression from a novel perspective of nonconvex optimization by designing an appropriate objective function. Then, we introduce NN-BCD, a block coordinate descent (BCD) algorithm to solve the nonconvex optimization. One advantage of our algorithm is that an efficient iteration scheme can be derived with closed-form, which is gradient-free. Therefore, our algorithm will not suffer from vanishing/exploding gradient problems. Furthermore, with the Kurdyka-{\L}ojasiewicz (K{\L}) property of our objective function, we show that our algorithm globally converges to a critical point at the rate of O(1/k), where k denotes the number of iterations. Lastly, extensive experiments with tensor train decomposition and weight pruning demonstrate the efficiency and superior performance of the proposed framework. Our code implementation is available at https://github.com/ChenyangLi-97/NN-BCD

Coronal mass ejections (CMEs) are massive solar eruptions, which have a significant impact on Earth. In this paper, we propose a new method, called DeepCME, to estimate two properties of CMEs, namely, CME mass and kinetic energy. Being able to estimate these properties helps better understand CME dynamics. Our study is based on the CME catalog maintained at the Coordinated Data Analysis Workshops (CDAW) Data Center, which contains all CMEs manually identified since 1996 using the Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory (SOHO). We use LASCO C2 data in the period between January 1996 and December 2020 to train, validate and test DeepCME through 10-fold cross validation. The DeepCME method is a fusion of three deep learning models, including ResNet, InceptionNet, and InceptionResNet. Our fusion model extracts features from LASCO C2 images, effectively combining the learning capabilities of the three component models to jointly estimate the mass and kinetic energy of CMEs. Experimental results show that the fusion model yields a mean relative error (MRE) of 0.013 (0.009, respectively) compared to the MRE of 0.019 (0.017, respectively) of the best component model InceptionResNet (InceptionNet, respectively) in estimating the CME mass (kinetic energy, respectively). To our knowledge, this is the first time that deep learning has been used for CME mass and kinetic energy estimations.

Solar flares, especially the M- and X-class flares, are often associated with coronal mass ejections (CMEs). They are the most important sources of space weather effects, that can severely impact the near-Earth environment. Thus it is essential to forecast flares (especially the M-and X-class ones) to mitigate their destructive and hazardous consequences. Here, we introduce several statistical and Machine Learning approaches to the prediction of the AR's Flare Index (FI) that quantifies the flare productivity of an AR by taking into account the numbers of different class flares within a certain time interval. Specifically, our sample includes 563 ARs appeared on solar disk from May 2010 to Dec 2017. The 25 magnetic parameters, provided by the Space-weather HMI Active Region Patches (SHARP) from Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), characterize coronal magnetic energy stored in ARs by proxy and are used as the predictors. We investigate the relationship between these SHARP parameters and the FI of ARs with a machine-learning algorithm (spline regression) and the resampling method (Synthetic Minority Over-Sampling Technique for Regression with Gaussian Noise, short by SMOGN). Based on the established relationship, we are able to predict the value of FIs for a given AR within the next 1-day period. Compared with other 4 popular machine learning algorithms, our methods improve the accuracy of FI prediction, especially for large FI. In addition, we sort the importance of SHARP parameters by Borda Count method calculated from the ranks that are rendered by 9 different machine learning methods.

Solar activity is usually caused by the evolution of solar magnetic fields. Magnetic field parameters derived from photospheric vector magnetograms of solar active regions have been used to analyze and forecast eruptive events such as solar flares and coronal mass ejections. Unfortunately, the most recent solar cycle 24 was relatively weak with few large flares, though it is the only solar cycle in which consistent time-sequence vector magnetograms have been available through the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) since its launch in 2010. In this paper, we look into another major instrument, namely the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) from 1996 to 2010. The data archive of SOHO/MDI covers more active solar cycle 23 with many large flares. However, SOHO/MDI data only has line-of-sight (LOS) magnetograms. We propose a new deep learning method, named MagNet, to learn from combined LOS magnetograms, Bx and By taken by SDO/HMI along with H-alpha observations collected by the Big Bear Solar Observatory (BBSO), and to generate vector components Bx' and By', which would form vector magnetograms with observed LOS data. In this way, we can expand the availability of vector magnetograms to the period from 1996 to present. Experimental results demonstrate the good performance of the proposed method. To our knowledge, this is the first time that deep learning has been used to generate photospheric vector magnetograms of solar active regions for SOHO/MDI using SDO/HMI and H-alpha data.