### Abstract

Machine learning and new AI 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 given set of input data is difficult to answer. Considering the unperturbed two-body problem, this paper investigates the approximation and prediction capabilities of three types of neural networks: Feed-Forward, Residual and Deep Residual. Used in a purely recurrent model, this three architectures are able to produce highly satisfactory performances, very close to numerical integration tolerances. 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 NN were able to better learn inherent dynamics characteristics in spherical coordinates without any apriori information than in Cartesian coordinate system. It is shown that a simple NN architecture is able to learn the symmetry of the central force and reproduce the conservation of the constants of the motion.

Original language | English (US) |
---|---|

Title of host publication | Spaceflight Mechanics 2019 |

Editors | Francesco Topputo, Andrew J. Sinclair, Matthew P. Wilkins, Renato Zanetti |

Publisher | Univelt Inc. |

Pages | 1789-1803 |

Number of pages | 15 |

ISBN (Print) | 9780877036593 |

State | Published - Jan 1 2019 |

Event | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 - Maui, United States Duration: Jan 13 2019 → Jan 17 2019 |

### Publication series

Name | Advances in the Astronautical Sciences |
---|---|

Volume | 168 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 |
---|---|

Country | United States |

City | Maui |

Period | 1/13/19 → 1/17/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Spaceflight Mechanics 2019*(pp. 1789-1803). [AAS 19-479] (Advances in the Astronautical Sciences; Vol. 168). Univelt Inc..

}

*Spaceflight Mechanics 2019.*, AAS 19-479, Advances in the Astronautical Sciences, vol. 168, Univelt Inc., pp. 1789-1803, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, Maui, United States, 1/13/19.

**Investigation of different neural network architectures for dynamic system identification : Applications to orbital mechanics.** / Guého, Damien; Singla, Puneet; Melton, Robert G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Investigation of different neural network architectures for dynamic system identification

T2 - Applications to orbital mechanics

AU - Guého, Damien

AU - Singla, Puneet

AU - Melton, Robert G.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Machine learning and new AI 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 given set of input data is difficult to answer. Considering the unperturbed two-body problem, this paper investigates the approximation and prediction capabilities of three types of neural networks: Feed-Forward, Residual and Deep Residual. Used in a purely recurrent model, this three architectures are able to produce highly satisfactory performances, very close to numerical integration tolerances. 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 NN were able to better learn inherent dynamics characteristics in spherical coordinates without any apriori information than in Cartesian coordinate system. It is shown that a simple NN architecture is able to learn the symmetry of the central force and reproduce the conservation of the constants of the motion.

AB - Machine learning and new AI 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 given set of input data is difficult to answer. Considering the unperturbed two-body problem, this paper investigates the approximation and prediction capabilities of three types of neural networks: Feed-Forward, Residual and Deep Residual. Used in a purely recurrent model, this three architectures are able to produce highly satisfactory performances, very close to numerical integration tolerances. 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 NN were able to better learn inherent dynamics characteristics in spherical coordinates without any apriori information than in Cartesian coordinate system. It is shown that a simple NN architecture is able to learn the symmetry of the central force and reproduce the conservation of the constants of the motion.

UR - http://www.scopus.com/inward/record.url?scp=85072959022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072959022&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072959022

SN - 9780877036593

T3 - Advances in the Astronautical Sciences

SP - 1789

EP - 1803

BT - Spaceflight Mechanics 2019

A2 - Topputo, Francesco

A2 - Sinclair, Andrew J.

A2 - Wilkins, Matthew P.

A2 - Zanetti, Renato

PB - Univelt Inc.

ER -