Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Designing Poisson integrators through machine learning
M. Vaquero, D. Martín de Diego, J. Cortés
IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Besancon, France, 2024, to appear
Abstract
This paper presents a general method to construct
Poisson integrators, i.e., integrators that preserve the
underlying Poisson geometry. We assume the Poisson
manifold is integrable, meaning there is a known local
symplectic groupoid for which the Poisson manifold
serves as the set of units. Our constructions build upon
the correspondence between Poisson diffeomorphisms and
Lagrangian bisections, which allows us to reformulate
the design of Poisson integrators as solutions to a
certain PDE (Hamilton-Jacobi). The main novelty of this
work is to understand the Hamilton-Jacobi PDE as an
optimization problem, whose solution can be easily
approximated using machine learning related
techniques. This research direction aligns with the
current trend in the PDE and machine learning
communities, as initiated by physics-informed neural
networks, advocating for designs that combine both
physical modeling (the Hamilton-Jacobi PDE) and data.
pdf
Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo