Machine Learning Applications in the Solar Interior and Atmosphere

Space weather is the study of the near-Earth impact of the processes on the Sun. In a this era of technology, space weather emerges as a crucial area of study wherein the state of the near-Earth conditions need to be modeled and forecasted. Crucially, the advent of machine learning provides us with opportunities to study this subject in a rather comprehensive manner. In this chapter, we treat the the processes arising from Sun to the impact on the ground as a set of coupled systems, which can be studied in isolation or in a coupled manner. We define these individual systems in terms of their state vector $\vec{S}$, which provides us with an opportunity to define the physical variables determining the system. This also allows us to consider the systems in terms of their observables, obtained through the action of operators as $\vec{O}[\vec{S}]$. In such a formalism, the machine learning algorithms serve as {\it learned operators}, defined generally as inference ($\mathcal{I}$), propagation ($\mathcal{P}$), and emulation ($\mathcal{E}$). Through such a formalism, we present how machine learning helps advance our understanding of the physical systems under study, while also accelerating the development of operational models for space weather forecasting.

The Solar wind is a continuous flow of charged particles emanating from the solar surface and governed by complex, interacting magnetohydrodynamic processes. Accurate specification of inner-boundary conditions is essential for heliospheric modeling and solar-wind prediction. In many practical applications, only a subset of interacting multi-field variables is directly available, but for a comprehensive view of solar wind prediction and downstream magnetohydrodynamic simulations, a more complete boundary state is required. In this work, we study the problem of learning the multi-field multi-scale solar magnetohydrodynamic state at 30 solar radii ($R_\odot$) using operator learning. Specifically, given the radial velocity and radial magnetic field, we aim to reconstruct the non-radial velocity and magnetic field components, radial and non-radial current density, thermodynamic density, and pressure components. This mapping is highly nonlinear, spatially coupled, and multi-scale, making it a challenging task for data-driven scientific machine learning. To address this problem, we employ a Local Neural Operator (LocalNO) that learns mappings between input and output function spaces while retaining locality and resolution-awareness. Unlike conventional regression models and autoencoder models, neural operators are better suited for learning structured field-to-field transformations arising from physical systems. The resulting predictions along with inputs are intended to serve as boundary condition variables for future inner-heliospheric modeling pipelines.

Solar energetic particle (SEP) events have attracted increasing attention due to their significant radiation hazards for aviation, spacecraft electronics, and human missions beyond Earth's magnetosphere. From a scientific perspective, SEP events are intriguing because they arise from a set of physical processes extending from the solar surface and corona through the heliosphere, offering insight into particle acceleration and transport mechanisms that are widely applicable across astrophysics. Therefore, advancing our ability to understand and predict SEP events is essential both for deepening our knowledge of such mechanisms and for safeguarding space technologies and exploration. Traditionally, researchers have modeled SEPs using physics-based simulations and empirical methods. More recently, machine learning (ML) has emerged as a new tool for understanding and predicting SEP events. The purpose of this manuscript is to review the currently available ML models for SEP prediction, identify the datasets used for training, compare their architectures, inputs, and outputs, and, based on these insights, outline good practices and recommendations for future research.