Orbit Classification and Sensitivity Analysis in Dynamical Systems Using Surrogate Models

Katharina Rath*, Christopher G. Albert, Bernd Bischl, Udo von Toussaint

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

Dynamics of many classical physics systems are described in terms of Hamilton’s equations. Commonly, initial conditions are only imperfectly known. The associated volume in phase space is preserved over time due to the symplecticity of the Hamiltonian flow. Here we study the propagation of uncertain initial conditions through dynamical systems using symplectic surrogate models of Hamiltonian flow maps. This allows fast sensitivity analysis with respect to the distribution of initial conditions and an estimation of local Lyapunov exponents (LLE) 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 the 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 the computation of fusion alpha particle losses
Original languageEnglish
Article number5
JournalPhysical Sciences Forum
Volume3
Issue number1
DOIs
Publication statusPublished - 5 Nov 2021
Externally publishedYes
Event40th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering - TU Graz, Virtuell, Graz, Austria
Duration: 4 Jul 20219 Jul 2021
Conference number: 14
https://www.tugraz.at/events/maxent2021/info/

Fields of Expertise

  • Information, Communication & Computing
  • Sustainable Systems

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