Physics Informed Neural Networks as addition to classical Precise Orbit Determination

Abstract
In recent years, the integration of artificial intelligence (AI), especially machine learning (ML), has found entrance in various fields, including industry, medicine, self-driving cars and daily life. However, the application of ML tools in space science is still in its early stages and holds the potential to complement traditional methods. This study investigates the effectiveness of machine learning algorithms, with a focus on Physics Informed Neural Networks (PINNs) to expand or support the classical methods in orbit propagation and determination.
PINNs were first introduced by Raissi et al. [1] and offer a promising avenue due to their unique ability to incorporate the governing differential equations of the system into the learning process, thereby imposing a physical constraint on the Networks predictions. This constraint enables effective training with sparse data, bypassing the need for large datasets typical for traditional Neural Network approaches. In addition, PINNs allow for the determination of unknown or poorly known parameters within the differential equation - a capability absent in conventional “Black-Box” Neural Networks.
To demonstrate the usefulness of PINNs, we first present a case study on simulated data within the framework of the AI4POD (Artificial Intelligence for Precise Orbit Determination) software tool of RSOs in the low earth orbit. A similar approach using Physics Informed Extreme Learning Machines was successfully conducted by Scorsoglio et al. [2] for simulated data. In contrast to this Single Layer architecture our approach incorporates a Deep Feed Forward Neural Network topology with a physics informed loss function. As a real case scenario, we
test the machine learning algorithm on data of the Rosetta mission [3] orbiting comet 67P/Churyumov-Gerasimenko and present preliminary results of the study.

Acknowledgements
The project Artificial Intelligence for Precise Orbit Determination (AI4POD) is funded by Deutsches Zentrum für Luft- und Raumfahrt, Bonn-Oberkassel, under grant 50LZ2308.

References
[1] M. Raissi, P. Perdikaris, G.E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,Journal of Computational Physics, Volume 378,2019, Pages 686-707, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2018.10.045
[2] Scorsoglio, A., Ghilardi, L. & Furfaro, R. A Physic-Informed Neural Network Approach to Orbit Determination. J Astronaut Sci 70, 25 (2023). https://doi.org/10.1007/s40295-023-00392-w
[3] Andert, T., Aigner, B., Dallinger, F., Haser, B., Pätzold, M., Hahn, M., 2024. Comparative Analysis of Data Preprocessing Methods for Precise Orbit Determination, in: EGU24-19558. Presented at the EGU General Assembly 2024, Vienna, Austria. https://doi.org/10.5194/egusphere-egu24-19558.