1. Introduction

Geomagnetic storms are significant physical phenomena caused by the prolonged interaction of the southward magnetic field in the solar wind with Earth's magnetic field, releasing a substantial amount of energy. This interaction intensifies the ring current in the Earth's magnetosphere, and when the current reaches critical levels, a geomagnetic storm is triggered [1]. These storms have profound impacts on human activities, particularly space operations, satellite communications, and power grids, making accurate prediction a crucial endeavor.

The increasing frequency of space activities and the critical reliance on satellite-based systems underscore the urgency of improving geomagnetic storm prediction capabilities. For instance, during the SpaceX Starlink satellite launch on February 3, 2022, a geomagnetic storm caused increased atmospheric drag, leading to the loss of 38 out of 49 satellites [2]. This incident highlighted the limitations of current prediction methods, which often fail to account for thermospheric expansion induced by geomagnetic storms. Such events emphasize the need for more precise and timely prediction methods to mitigate risks associated with space weather.

Current prediction methods for geomagnetic storms can be broadly categorized into three broad categories: physical models, statistical models, and machine learning methods. Physical models simulate the dynamic interactions between the solar wind and Earth's magnetosphere, leveraging magnetohydrodynamic (MHD) equations to predict geomagnetic disturbances [3][4]. Statistical models rely on historical data to identify patterns and estimate storm probabilities [5]. Machine learning methods have recently emerged as powerful tools for capturing complex nonlinear relationships in high-dimensional data [6]. Each of these approaches has its strengths and limitations. Physical models provide a robust theoretical framework but are computationally intensive and reliant on high-quality input data. Statistical models are computationally efficient but struggle with capturing nonlinear dynamics, whereas machine learning methods excel in handling large-scale data, but face challenges related to data quality, interpretability, and computational demands.

To address these challenges, integrating these methodologies presents a promising pathway to enhance prediction accuracy and timeliness. Hybrid models that combine the theoretical foundation of physical models, the probabilistic insights of statistical approaches, and the nonlinear modeling capabilities of machine learning can address the individual shortcomings of each method. Such integration is not only feasible but also necessary to develop reliable, real-time prediction systems capable of mitigating the risks posed by geomagnetic storms.

This paper aims to provide a comprehensive review of geomagnetic storm prediction methods, systematically analyzing the principles, advantages, and limitations of physical models, statistical models, and machine learning approaches. By highlighting recent advancements and exploring potential pathways for integrating these methods, this study seeks to offer insights into optimizing prediction accuracy and timeliness, ultimately contributing to the development of more robust space weather early warning systems.

2. The Current Development Status of Geomagnetic Storm Prediction Techniques

2.1. Physical Model

Physics-based geospace models are essential tools for predicting geomagnetic storms. The core principle lies in solving the magnetohydrodynamics (MHD) equations, which describe the complex interactions among the solar wind, the interplanetary magnetic field (IMF), and the Earth's magnetosphere-ionosphere system. Key driving conditions include solar wind parameters such as velocity, density, and temperature, the southward component of the IMF (Bs), and the tilt angle of the Earth's magnetic field as driving conditions. Through numerical simulations, they reproduce the processes of magnetic reconnection, plasma flows, and the evolution of current systems [7]. For example, the Lyon-Fedder-Mobarry (LFM) model utilizes MHD equations to simulate the interaction between the solar wind and the Earth's magnetosphere. It accurately calculates polar currents and ionospheric conductance through the Magnetosphere-Ionosphere Coupler (MIX). The OpenGGCM model, as a global MHD model, focuses on high-resolution simulations of the coupled processes among the solar wind, magnetosphere, ionosphere, and thermosphere systems. The Space Weather Modeling Framework (SWMF) provides multi-domain physical simulation capabilities from the Sun to the Earth, making it suitable for studying comprehensive space weather phenomena [8]. By integrating real-time solar wind observations, such as data from NASA's ACE satellite, these models can provide short-term geomagnetic disturbance forecasts with lead times of 15 to 30 minutes, offering crucial support for the early warning of extreme geomagnetic storms.

However, despite their strong explanatory power, the reliance on high-quality input data and the high computational complexity of physical models limits their real-time applicability. Enhancements are needed to address these limitations, especially when predicting complex events or dynamic processes [9].

2.2. Statistical Model

Statistical models, based on system identification methods, treat the magnetosphere-ionosphere system as a low-dimensional input-output nonlinear dynamical system. These models focus on analyzing observational data (such as solar wind and the Dst index) to directly identify the system’s dynamic behavior, rather than relying on complex physical equations [3]. For example, the NARMAX model is widely used to construct a dynamic behavior framework for the geomagnetic index Dst. Similarly, the Volterra model and its variants are often employed as effective tools for describing the nonlinear dynamics of the magnetosphere.

Statistical models effectively capture the historical trends of geomagnetic disturbances based on observational data, making them suitable for medium- and small-scale events. However, statistical models also have certain limitations: when dealing with nonlinear and complex coupled processes, such as magnetic reconnection, they struggle to provide accurate physical representations [9]. This restricts their predictive accuracy in highly dynamic or large-scale events.

2.3. Machine Learning

Machine learning methods have rapidly advanced in geomagnetic storm prediction, showing significant advantages and potential. By standardizing observational data and employing techniques such as correlation analysis and feature importance analysis, key predictive features, such as variations in the Bz component and solar wind speed, can be identified. Based on these selected features, suitable machine learning models are then applied for prediction. For instance, Artificial Neural Networks (ANN) are effective at capturing complex nonlinear relationships, Support Vector Machines (SVM) are well-suited for classification tasks with small-scale datasets, and models like Random Forests (RF) and Gradient Boosting (XGBoost) are commonly used for feature importance analysis and the prediction of geomagnetic storm events [10]. In addition, emerging methods such as Convolutional Neural Networks (CNN) have gradually been applied in recent years, particularly excelling in global geomagnetic field modeling and prediction [11].

Machine learning methods offer several advantages, including the ability to capture complex nonlinear relationships, excellent performance in handling large-scale data and high-dimensional features, and applicability for both short-term and long-term predictions. However, these methods also have some limitations, such as high sensitivity to data quality, limited interpretability (especially for deep learning models), and substantial computational resource requirements [10]. Despite these challenges, machine learning has become a novel and rapidly evolving tool in the field of geomagnetic storm prediction, providing crucial support for enhancing prediction accuracy and efficiency.

3. Optimization Strategies for Geomagnetic Storm Prediction Methods

3.1. Improve the Accuracy

Existing geomagnetic storm prediction methods have limitations in terms of equipment, data, and model performance. For instance, the NOAA Space Weather Prediction Center (SWPC) model has achieved moderate success in geomagnetic storm prediction, but it performs inadequately in classification accuracy, especially in classifying geomagnetic storms. In SWPC's one-day forecast, the model achieves only 61% accuracy in classifying geomagnetic storms [12]. In recent years, there has been significant effort to improve the accuracy of geomagnetic storm prediction, with many new feasible methods being explored. These advancements are discussed in this review, with the hope that they will provide valuable insights and guidance for future research in the field.

One such approach involves use of a Gaussian Kernel Support Vector Machine (G-SVM). This method incorporates a Gaussian kernel function (also known as the Radial Basis Function, RBF) to handle nonlinear data, eliminating the need for costly magnetometers or solar wind measurement devices. Instead, it relies on analyzing solar images captured by a single satellite, such as NASA’s Solar Dynamics Observatory (SDO) for predictions [12]. It is capable of handling complex nonlinear data, representing an improvement over traditional linear models. However, the method has its drawbacks: image noise or insufficient data can significantly affect the model's performance, and the model can only predict geomagnetic storm events for the next 24 hours. Currently, G-SVM achieves an overall classification accuracy of 76%, but its performance in detecting the “geomagnetic storm present” category remains inadequate, highlighting the need for further refinement.

Another promising development is a deep learning model based on spherical harmonic decomposition for global geomagnetic field modeling [13]. The method uses spherical harmonic basis functions to approximate geomagnetic field disturbances, mapping the original complex geomagnetic data into spherical harmonic space. This reduces the data dimensions while preserving important geomagnetic information. Besides, Lasso regression is applied to regularize and reduce the redundancy of spherical harmonic coefficients, preventing overfitting and improving the model's generalization ability. Unlike traditional methods, this approach does not rely on high-cost equipment (such as space probes) while offering higher spatiotemporal resolution for geomagnetic storm monitoring. However, although spherical harmonic decomposition reduces the data dimensions, it introduces many higher-order spherical harmonic coefficients. The optimization of these coefficients requires additional regularization such as Lasso regression, otherwise, it may lead to overfitting or mode coupling issues. Moreover, the assumption of a smooth global geomagnetic field may limit the model’s ability to capture short-duration or localized geomagnetic storm events.

There has also been significant research into the prediction of short-term, localized geomagnetic storms. A hybrid deep learning model combining Convolutional Neural Networks (CNN), Gated Recurrent Units (GRU), and Long Short-Term Memory (LSTM) networks, known as C-G-LSTM, has been developed to predict short-term, localized geomagnetic storms. This model can forecast the changes in the Dst index for the next 1 to 6 hours. The method performs exceptionally well during short-term and intense geomagnetic storm events: for a 1-hour forecast, the Root Mean Square Error (RMSE) is approximately 3.4 nT with an R-value close to 0.98; for a 6-hour forecast, the RMSE increases to 7.3 nT, with an R-value still as high as 0.88. This approach shows promise as a research direction for short-term geomagnetic storm prediction [14].

Hybrid models that combine physical models, such as NOAA’s Geospace model, with machine learning algorithms like boosted classification trees are another noteworthy innovation. This hybrid approach leverages the theoretical foundation of physical models and the nonlinear modeling capability of machine learning, addressing the limitations of each method. Under high-threshold conditions (i.e., during intense geomagnetic storm events), the model significantly reduces both false alarm rates and missed event rates [15]. However, systematic errors in the physical model, such as underestimating large disturbances and overestimating small disturbances, and the challenge of balancing the outputs of the physical and machine learning components, remain unresolved. Additionally, real-time prediction capabilities are still limited. In the future, improving the quality and accuracy of the input physical model, along with combining more efficient physical models and machine learning techniques, could enhance prediction accuracy.

3.2. Improve Timeliness

Improving the timeliness of geomagnetic storm predictions is equally, if not more, critical than improving accuracy. Current predictions are limited by the measurement frequency of the Kp index (measured every 3 hours), which makes it difficult to extend the prediction lead time further. The current 3-hour lead forecast is already close to the practical limit of existing technology, and further predictions may not yield satisfactory results due to insufficient temporal resolution of the data [16].

One current approach is to use solar observation data instead of traditional solar wind detectors to directly predict geomagnetic storms driven by high-speed solar wind streams (HSS). This method can extend the prediction lead time to several days, showing significant potential for practical applications [17]. Although promising, this approach depends heavily on high-resolution observational tools for solar data, such as the size of coronal holes and magnetic field polarity, which are currently limited in availability and adaptability. This approach is still in the validation and research phase.

Another approach is to use a Long Short-Term Memory (LSTM) deep learning model, combined with uncertainty quantification techniques, to perform short-term predictions of the geomagnetic storm index (SYM-H) over periods ranging from 0.5 to 5 hours. While this approach demonstrates potential for improving short-term forecasts, the computational requirements and data processing times pose challenges to achieving real-time warning capability. Additionally, since the data is derived from specific periods and solar activity conditions, the model's predictive ability may lack adaptability to other periods or different solar cycles [18].

Timeliness can be improved through expanded deployment of real-time observation instruments. Satellite constellations and instruments placed at solar-terrestrial Lagrange points (such as L1) could provide continuous monitoring of solar wind, IMF, and other relevant parameters, thereby enhancing early detection capabilities for geomagnetic storms. At the same time, collaborative observations using satellite constellations can provide more comprehensive space weather data. Integrating multi-source observational data (such as real-time data from NASA's ACE satellite and SDO) can improve the timeliness and completeness of the data. By combining advanced data assimilation algorithms, observational data can be promptly fed into prediction models, further enhancing the models' responsiveness.

4. Future Direction

To enhance the accuracy and timeliness of geomagnetic storm prediction, integrating physical models, statistical models, and machine learning methods offers a promising direction. Physical models provide a robust theoretical framework by simulating solar wind-magnetosphere interactions. Statistical models excel in capturing historical trends and probabilistic characteristics. Machine learning methods contribute by modeling complex nonlinear relationships and handling large-scale, high-dimensional data. A hybrid approach could involve using physical models to generate initial conditions or constrain boundary parameters, statistical models to identify historical patterns, and machine learning techniques to refine predictions and adjust dynamically based on real-time data.

For example, combining physical models for global geomagnetic simulations with machine learning algorithms for localized, short-term predictions can address both spatial and temporal resolution challenges. Techniques such as transfer learning, data assimilation, and hybrid gray-box modeling can further optimize model performance by leveraging the strengths of each approach. Such integrations have the potential to significantly improve prediction accuracy, particularly for extreme geomagnetic events, and enhance the responsiveness of early warning systems.

It is important to note that the success of these methods depends heavily on the quality of the input data. Therefore, while optimizing the models, continuous efforts must also be made to enhance the precision of detection tools to provide more complete and accurate data support. Moreover, most models still exhibit significant prediction errors during the extreme peak phases of geomagnetic storms, with relatively poor performance in predicting intense geomagnetic storm events. To address this, a deeper analysis of the patterns of extreme geomagnetic storms should be conducted, summarizing their characteristics and incorporating these patterns into model development to further improve the predictive capabilities of models under extreme conditions.

5. Conclusion

Geomagnetic storms, caused by solar wind and coronal mass ejections, significantly impact Earth's magnetosphere and ionosphere, posing risks to space activities and satellite operations. This review explores three primary prediction approaches: physical models, statistical models, and machine learning methods. Physical models provide theoretical explanations but face challenges with high computational complexity and reliance on real-time data. Statistical models, while simpler and cost-effective, struggle with nonlinearity and complex dynamics. Machine learning methods, particularly hybrid and deep learning models, show promise in handling nonlinear relationships and short-term predictions but face limitations in interpretability, data quality dependence, and real-time performance.

Efforts to enhance accuracy and timeliness have led to innovations, including integrating solar observation data, spherical harmonic decomposition, and hybrid gray-box models. Real-time prediction improvements focus on deploying advanced observation instruments, utilizing multi-source data, and adopting high-performance computational techniques. However, most methods remain constrained by data limitations and perform inadequately during extreme geomagnetic events. Future research should address these challenges by improving input data quality, leveraging extreme event patterns, and developing adaptable models to ensure more accurate and timely predictions of geomagnetic storms. By advancing these strategies, the field can move closer to achieving reliable, real-time geomagnetic storm predictions, supporting the safety and resilience of space activities and critical infrastructure.