SISSA Colloquium - The synergy between perturbative methods and machine learning techniques in Celestial Mechanics - Alessandra Celletti

ABSTRACT Classical perturbation theory is a cornerstone of Celestial Mechanics, since it allows one to determine an approximate solution of the dynamics. It applies typically to nearly-integrable Hamiltonian systems. Further developments of perturbation theory are represented by KAM theory and Nekhoroshev's theorem. All these mathematical theories have been successfully applied to investigate stability in models of Celestial
Mechanics and Astrodynamics. In some cases, they can even give results in dissipative systems, most notably the so-called conformally symplectic systems, which enjoy important geometric properties.
As a complement of the analytical studies, machine learning methods can be used to get information on the dynamics. These techniques have been used to classify  regular and chaotic motions in satellite's rotational dynamics and to cluster space debris after a break-up event. These results have the potential to pave the way to a synergetic use of perturbative and ML methods.

Alessandra Celletti received her PhD in 1989 at the Swiss Federal Institute of Technology in Zurich (ETH) under the supervision of Jürgen Moser and Jörg Waldvogel. She is currently Full Professor of Mathematical Physics at the University of Rome Tor Vergata; since 2020 she is member of the governing board and vice-President of ANVUR. Her research interests concern Celestial Mechanics and Dynamical Systems with particular reference to perturbative methods and KAM theory with applications to Solar system dynamics. She is a founding member of the Italian Society of Celestial Mechanics and Astrodynamics, which she chaired from 2001 to 2013. Since 2010 she has been an honorary member of the "Celestial Mechanics Institute". In 2018 became President of the Scientific Committee in Celestial Mechanics of the International Astronomical Union, while in 2019 she has been named in the Governing Board of the Italian Space Agency (until 2020). In 2023 she has been awarded the “Dirk Brouwer Career Award” from the American Astronomical Society. The asteroid 117539 bears her name