Finding Real-World Orbital Motion Laws from Data
João Funenga Marta Guimarães Henrique Costa Cláudia Soares
A novel approach is presented for discovering PDEs that govern the motion of
satellites in space. The method is based on SINDy, a data-driven technique
capable of identifying the underlying dynamics of complex physical systems from
time series data. SINDy is utilized to uncover PDEs that describe the laws of
physics in space, which are non-deterministic and influenced by various factors
such as drag or the reference area (related to the attitude of the satellite).
In contrast to prior works, the physically interpretable coordinate system is
maintained, and no dimensionality reduction technique is applied to the data.
By training the model with multiple representative trajectories of LEO -
encompassing various inclinations, eccentricities, and altitudes - and testing
it with unseen orbital motion patterns, a mean error of around 140 km for the
positions and 0.12 km/s for the velocities is achieved. The method offers the
advantage of delivering interpretable, accurate, and complex models of orbital
motion that can be employed for propagation or as inputs to predictive models
for other variables of interest, such as atmospheric drag or the probability of
collision in an encounter with a spacecraft or space objects. In conclusion,
the work demonstrates the promising potential of using SINDy to discover the
equations governing the behaviour of satellites in space. The technique has
been successfully applied to uncover PDEs describing the motion of satellites
in LEO with high accuracy. The method possesses several advantages over
traditional models, including the ability to provide physically interpretable,
accurate, and complex models of orbital motion derived from high-entropy
datasets. These models can be utilised for propagation or as inputs to
predictive models for other variables of interest.