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
  • Robert Graham Melton, Thesis 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.