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The Space Domain Awareness (SDA) community routinely tracks satellites in orbit by fitting an orbital state to observations made by the Space Surveillance Network (SSN). In order to fit such orbits, an accurate model of the forces that are acting on the satellite is required. Over the past several decades, high-quality, physics-based models have been developed for satellite state estimation and propagation. These models are exceedingly good at estimating and propagating orbital states for non-maneuvering satellites; however, there are several classes of anomalous accelerations that a satellite might experience which are not well-modeled, such as satellites that use low-thrust electric propulsion to modify their orbit. Physics-Informed Neural Networks (PINNs) are a valuable tool for these classes of satellites as they combine physics models with Deep Neural Networks (DNNs), which are highly expressive and versatile function approximators. By combining a physics model with a DNN, the machine learning model need not learn astrodynamics, which results in more efficient and effective utilization of machine learning resources. This paper details the application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites. The PINN is trained to learn the unknown acceleration by minimizing the mean square error of observations. We evaluate the performance of pure physics models with PINNs in terms of their observation residuals and their propagation accuracy beyond the fit span of the observations. For a two-day simulation of a GEO satellite using an unmodeled acceleration profile on the order of $10^{-8} \text{ km/s}^2$, the PINN outperformed the best-fit physics model by orders of magnitude for both observation residuals (123 arcsec vs 1.00 arcsec) as well as propagation accuracy (3860 km vs 164 km after five days).

RR Lyrae variable stars have long been reliable standard candles used to discern structure in the Local Group. With this in mind, we present a routine to identify groupings containing a statistically significant number of RR Lyrae variables in the Milky Way environment. RR Lyrae variable groupings, or substructures, with potential Galactic archaeology applications are found using a forest of agglomerative, hierarchical clustering trees, whose leaves are Milky Way RR Lyrae variables. Each grouping is validated by ensuring that the internal RR Lyrae variable proper motions are sufficiently correlated. Photometric information was collected from the Gaia second data release and proper motions from the (early) third data release. After applying this routine to the catalogue of 91234 variables, we are able to report sixteen unique RR Lyrae substructures with physical sizes of less than 1 kpc. Five of these substructures are in close proximity to Milky Way globular clusters with previously known tidal tails and/or a potential connection to Galactic merger events. One candidate substructure is in the neighbourhood of the Large Magellanic Cloud but is more distant (and older) than known satellites of the dwarf galaxy. Our study ends with a discussion of ways in which future surveys could be applied to the discovery of Milky Way stellar streams., Comment: 15 pages, 7 figures, 3 tables (including appendices). Accepted for publication in MNRAS