Machine learning applications in the heliosphere

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.