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Designing Poisson Integrators Through Machine Learning
April 1, 2024, 4:42 a.m. | Miguel Vaquero, David Mart\'in de Diego, Jorge Cort\'es
cs.LG updates on arXiv.org arxiv.org
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 …
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