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


Core Concepts
Data-driven framework for global linearization of Two-Body and Circular Restricted Three-Body Problems using Koopman Theory.
Abstract
The study focuses on the importance of understanding celestial and artificial satellite motion in aerospace engineering. It proposes a data-driven framework for system identification and global linearization of orbital problems using deep learning-based Koopman Theory. The method can accurately learn the dynamics of Two-Body and Circular Restricted Three-Body Problems, showcasing its ability to generalize to various systems without retraining. The approach aims to simplify control systems for satellites by achieving a globally linear representation of their dynamics.
Stats
Global linearization allows engineers to control satellite systems efficiently. Deep learning-based Koopman Theory identifies underlying dynamics. Data-driven methods like Extended Dynamic Mode Decomposition are used for approximation. Neural Networks with custom architecture approximate Koopman operator.
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Deeper Inquiries

How does the proposed data-driven framework compare to traditional methods in terms of accuracy and efficiency

The proposed data-driven framework for dynamics identification and linearization using Koopman Theory offers several advantages over traditional methods in terms of accuracy and efficiency. Firstly, the deep learning-based approach allows for the discovery of a globally linear representation of nonlinear systems, eliminating the need for frequent linearizations around specific operating points. This results in more accurate predictions and reduced computational costs when performing control maneuvers. Secondly, by utilizing neural networks to learn observable functions that are used to approximate the Koopman operator, the model can capture complex dynamics without requiring manual selection of basis functions. This automated feature extraction leads to improved accuracy in modeling orbital systems. Additionally, the framework's ability to generalize across different orbits without retraining is a significant advantage. The model can accurately predict trajectories for various two-body systems with minimal additional training required. Overall, compared to traditional methods that rely on manual system identification and linearization techniques, the data-driven framework based on deep learning offers higher accuracy and efficiency in capturing complex orbital dynamics.

What challenges may arise when applying this approach to more complex orbital systems beyond the ones studied

When applying this approach to more complex orbital systems beyond those studied (such as Circular Restricted Three-Body Problems), several challenges may arise: Increased Dimensionality: More complex orbital systems often involve higher-dimensional state spaces, leading to larger datasets and longer training times for neural networks. Nonlinear Dynamics: Complex gravitational interactions or perturbations in multi-body systems can introduce nonlinearity that may be challenging for neural networks to accurately capture. Model Generalization: Ensuring that a model trained on one set of initial conditions can effectively generalize to unseen scenarios or different central bodies requires careful validation and testing procedures. Data Availability: Obtaining sufficient high-quality data for training models on intricate orbital problems may be challenging due to limited observations or simulations available. Interpretability: Deep learning models are often considered black boxes, making it difficult to interpret how they arrive at certain predictions or decisions in highly complex scenarios like celestial mechanics.

How can the concept of global linearization through deep learning be applied to other fields outside aerospace engineering

The concept of global linearization through deep learning can be applied beyond aerospace engineering into various other fields such as robotics, finance, climate modeling, and healthcare: In robotics: Deep learning could be used to develop globally-linearized models for robot motion planning and control tasks involving multiple interacting agents or dynamic environments. In finance: Predictive models based on global linearization could help analyze stock market trends or optimize trading strategies by capturing underlying nonlinear dynamics efficiently. In climate modeling: Applying deep learning techniques for global linearization could enhance weather forecasting accuracy by creating more robust predictive models from large-scale atmospheric data sets. 4 .In healthcare: Global linearization through deep learning could aid in predicting disease progression patterns or optimizing treatment plans based on patient-specific data while considering nonlinear interactions within biological systems.
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