# Deep Learning Based Dynamics Identification and Linearization of Orbital Problems using Koopman Theory

arXiv: https://arxiv.org/abs/2403.08965 · HTML: https://mlsanity.com/paper/2403.08965/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 13 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control](https://mlsanity.com/paper/1911.08751/) (2019)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [Data-Driven Models for Control Engineering Applications Using the Koopman Operator](https://mlsanity.com/paper/2112.07983/) (2021)
- [Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Control](https://mlsanity.com/paper/2309.04074/) (2023)
- [Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition](https://mlsanity.com/paper/2110.08442/) (2021)
- [A Koopman-Operator Control Optimization for Relative Motion in Space](https://mlsanity.com/paper/2207.07079/) (2022)

## Built on by (most cited first, 3 of 3)

- [Customize Segment Anything Model for Multi-Modal Semantic Segmentation with Mixture of LoRA Experts](https://mlsanity.com/paper/2412.04220/) (2024)
- [Leveraging KANs For Enhanced Deep Koopman Operator Discovery](https://mlsanity.com/paper/2406.02875/) (2024)
- [Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics](https://mlsanity.com/paper/2607.20235/) (2026)

## Abstract (arXiv)

The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing demand for satellites and satellite formation flying, fast and efficient control of these systems is becoming ever more important. Global linearization of these systems allows engineers to employ methods of control in order to achieve these desired results. We propose a data-driven framework for simultaneous system identification and global linearization of the Circular, Elliptical and Perturbed Two-Body Problem as well as the Circular Restricted Three-Body Problem around the L1 Lagrange point via deep learning-based Koopman Theory, i.e., a framework that can identify the underlying dynamics and globally linearize it into a linear time-invariant (LTI) system. The linear Koopman operator is discovered through purely data-driven training of a Deep Neural Network with a custom architecture. This paper displays the ability of the Koopman operator to generalize to various other Two-Body systems without the need for retraining. We also demonstrate the capability of the same architecture to be utilized to accurately learn a Koopman operator that approximates the Circular Restricted Three-Body Problem.