Hybrid Modeling of the N-Body Problem with Applications to Astrophysics

Abstract

Over the last years, the field of hybrid modeling, the concept of combining data-driven machine learning models and numerical solution methods to simulate a physical system, has seen an immense increase in research. This new paradigm within modeling uses its predictor capabilities from neural networks to uncover the unknown physics of the underlying system, and bridges these hidden physics with the strong mathematical foundation of numerical integrators and the governing equations of the physical system. Even though hybrid modeling is being introduced into many different fields of research, one field which so far has lacked a more detailed investigation is the field of n-body problems. This field also represents the class of non-linear systems of O.D.Es. with symplectic structure. The n-body problem has through the ages been a source of countless scientific discoveries and is still of great interest to this day. As an application, this thesis will look at the problem of n-body dynamics of planetary motion, more specifically, the simulation of the main celestial bodies of the Solar System. As the first to create a hybrid model for the n-body problem of more than 3 bodies, this thesis will show, through a series of important observations and modeling approaches, that hybrid modeling of the n-body problem can be achieved. The results will also show that the subsequent model can improve the results of a standard physics-based model, the standardized modeling approach for the n-body problem. To the best of the author’s knowledge, this thesis will also be the first to present a pure data-driven model for predicting the orbital motion of planets in our Solar System.