Ionospheric scientists have amassed huge collections of image data for auroral arcs that extend around the Earth's poles. However, the high costs of in situ electromagnetic data for these auroral arcs are a major barrier to drawing definitive conclusions about how auroral arcs are shaped by ionospheric conditions. Another problem for in situ data is measurement noise, which, after interpolation, can cause spurious divergence features in a field that is should be divergence-free. To optimize use of data from scientific satellites, we aim to combine interpolation schemes with physical constraints to extract sub-grid information from multipoint data. One such constraint is numerically enforcing the electrostatic approximation that Curl(E) = 0, meaning that divergence of flow is zero for a stable arc: Div(V) = 0. Additionally, one can impose that Div(B) must be zero for all data. Although numerous methods exist to interpolate sub grid information, their solutions may not always be divergence-free in source-free regions, resulting in large numerical errors. This thesis assesses divergence-free constrained, Radial Basis Function (RBF) interpolation methods to formulate a more robust representation of sub-grid information for the in situ data. Artificial data and experimental data are used to test and validate the implementation and accuracy of each proposed technique. By increasing the in situ data's effective density to match auroral image datasets, we aim to train Machine Learning (ML) algorithms to predict electromagnetic events from ground based auroral imagery.