Learning Capabilities of Neural Network and Keplerian Dynamics
Open Access
- Author:
- Gueho, Damien
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- April 08, 2019
- Committee Members:
- Puneet Singla, Thesis Advisor/Co-Advisor
Robert Graham Melton, Thesis Advisor/Co-Advisor - Keywords:
- Machine Learning
Artificial intelligence
Neural Network
capabilities
Learn
two-body problem
residual neural network
feed-forward neural network
dynamic system
dynamical system
approximation
prediction
recurrent model
data set - Abstract:
- Machine learning and new artificial intelligence algorithms inspire the scientific community to explore and develop new approaches for discovery of scientific laws and governing equations for complex physical and nonlinear dynamical systems. The question on how well deep learning approaches can approximate a dynamic system given a set of input data is difficult to answer. Neural networks have garnered significant attention in the last decade but it is not clear how well these tools can learn the inherent characteristics of a dynamical model (such as conservation laws) from training data only. Considering the unperturbed Keplerian two-body problem, this work investigates the approximation and prediction capabilities of neural networks in learning dynamical system models in a purely recurrent model. Training neural networks with data from a single revolution around an orbit produces poor performance when predicting motion on subsequent revolutions. By incorporating deviations from constancy of angular momentum and total energy into the objective function for the neural network model, predictive performance improves significantly. Further improvements appear when a richer training data set (generated from a number of orbits with different orbital element values) is employed or with different structures such as residual or deep residual architectures. Furthermore, the effect of the mathematical representation (i.e. coordinate system) on the learning process is also investigated. From numerical results, it can be inferred that neural networks were able to better learn inherent dynamics characteristics in spherical coordinates without any apriori information than in a Cartesian coordinate system. It is shown that a simple architecture is able to learn the symmetry of the central force and reproduce the conservation of the constants of the motion.