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author={Kevin Otto and Simon Burgis and Kristian Kersting and Reinhold Bertrand and Devendra Singh Dhami},
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note = {The number of satellites in orbit around Earth is increasing rapidly, with
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the risk of collision rising accordingly. Trends of the global population of satellites
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need to be analyzed to test the viability and impact of proposed rules and laws
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affecting the satellite population and collision avoidance strategies. This requires
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large scale simulations of satellites that are propagated on long timescales to compute
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the large amounts of actionable close encounters (called conjunctions), which could
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lead to collisions. Rigorously checking for conjunctions by computing future states of
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orbits is computationally expensive due to the large amount of objects involved and
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conjunction filters are thus used to remove non-conjuncting orbit pairs from the list
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of possible conjunctions. In this work, we explore the possibility of machine learning
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(ML) based conjunction filters using several algorithms such as eXtreme Gradient
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Boosting, TabNet and (physics-informed) neural networks and deep operator networks.
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To show the viability and the potential of ML based filters, these algorithms are
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trained to predict the future state of orbits. For the physics-informed approaches,
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multiple partial differential equations are set up using the Kepler equation as a basis.
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The empirical results demonstrate that physics-informed deep operator networks are
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capable of predicting the future state of orbits using these equations (RMSE: 0.136) and
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outperform eXtreme Gradient Boosting (RMSE: 0.568) and TabNet (RMSE: 0.459).
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We also propose a filter based on the trained deep operator network which is shown
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to outperforms the filter capability of the commonly used perigee-apogee test and the
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orbit path filter on a synthetic dataset, while being on average 3.2 times faster to
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compute than a rigorous conjunction check.},
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+
Journal = {Machine Learning: Science and Technology (MLST)},
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note = {The number of satellites in orbit around Earth is increasing rapidly, with the risk of collision rising accordingly. Trends of the global population of satellites
400
+
need to be analyzed to test the viability and impact of proposed rules and laws affecting the satellite population and collision avoidance strategies. This requires
401
+
large scale simulations of satellites that are propagated on long timescales to compute the large amounts of actionable close encounters (called conjunctions), which could
402
+
lead to collisions. Rigorously checking for conjunctions by computing future states of orbits is computationally expensive due to the large amount of objects involved and
403
+
conjunction filters are thus used to remove non-conjuncting orbit pairs from the list of possible conjunctions. In this work, we explore the possibility of machine learning
404
+
(ML) based conjunction filters using several algorithms such as eXtreme Gradient Boosting, TabNet and (physics-informed) neural networks and deep operator networks.
405
+
To show the viability and the potential of ML based filters, these algorithms are trained to predict the future state of orbits. For the physics-informed approaches,
406
+
multiple partial differential equations are set up using the Kepler equation as a basis. The empirical results demonstrate that physics-informed deep operator networks are
407
+
capable of predicting the future state of orbits using these equations (RMSE: 0.136) and outperform eXtreme Gradient Boosting (RMSE: 0.568) and TabNet (RMSE: 0.459).
408
+
We also propose a filter based on the trained deep operator network which is shown to outperforms the filter capability of the commonly used perigee-apogee test and the
409
+
orbit path filter on a synthetic dataset, while being on average 3.2 times faster to compute than a rigorous conjunction check.},
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title={Machine Learning meets Kepler: Inverting Kepler’s Equation for All vs All Conjunction Analysis},
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