SMuK 2021 – scientific programme
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P: Fachverband Plasmaphysik
P 17: Poster II
P 17.36: Poster
Friday, September 3, 2021, 14:00–16:00, P
Orbit classification in Hamiltonian systems using surrogate models — •Katharina Rath1,2, Christopher G. Albert2, Bernd Bischl1, and Udo von Toussaint2 — 1Ludwig-Maximilians-Universität München, Munich, Germany — 2Max-Planck-Institut für Plasmaphysik, Garching, Germany
Discrete representations of Hamiltonian systems require structure-preserving properties in order to preserve invariants of motion and orbit topology in phase space. Here we employ a fast symplectic surrogate model based on Gaussian process regression that is used to compute evolving system states over long periods of time. The Jacobian is directly available from the surrogate model and allows therefore an estimation of local Lyapunov exponents (LLEs) that give insight into local predictability of a dynamical system. In Hamiltonian systems, LLEs permit a distinction between regular and chaotic orbits. Combined with Bayesian methods we provide a statistical analysis of local stability and sensitivity in phase space for Hamiltonian systems.
The intended application is early classification of regular and chaotic orbits of fusion alpha particles in stellarator reactors. The degree of stochastization during a given time period is used as an estimate for the probability that orbits of a specific region in phase space are lost at the plasma boundary. Thus, the approach offers a promising way to accelerate computation of fusion alpha particle losses.