Display options
Cite
Tschöpe M, Feldmaier M, Main J, et al. Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems. Phys Rev E. 2020;101(2):022219doi: 10.1103/PhysRevE.101.022219.
Tschöpe, M., Feldmaier, M., Main, J., & Hernandez, R. (2020). Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems. Physical review. E, 101(2), 022219. https://doi.org/10.1103/PhysRevE.101.022219
Tschöpe, Martin, et al. "Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems." Physical review. E vol. 101,2 (2020): 022219. doi: https://doi.org/10.1103/PhysRevE.101.022219
Tschöpe M, Feldmaier M, Main J, Hernandez R. Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems. Phys Rev E. 2020 Feb;101(2):022219. doi: 10.1103/PhysRevE.101.022219. PMID: 32168686.
Copy Download .nbib Format: NLM
Share it on

Phys Rev E. 2020 Feb;101(2):022219. doi: 10.1103/PhysRevE.101.022219.

Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems.

Physical review. E

Martin Tschöpe, Matthias Feldmaier, Jörg Main, Rigoberto Hernandez

Affiliations

  1. Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany.
  2. Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.

PMID: 32168686 DOI: 10.1103/PhysRevE.101.022219

Abstract

Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never leave this manifold when propagated forward or backward in time. However, the numerical investigation of the dynamics on the NHIM is difficult because of the instability of the motion. We apply a neural network to describe time-dependent NHIMs and use this network to stabilize the motion on the NHIM for a periodically driven model system with two degrees of freedom. The method allows us to analyze the dynamics on the NHIM via Poincaré surfaces of section (PSOS) and to determine the transition-state (TS) trajectory as a periodic orbit with the same periodicity as the driving saddle, viz. a fixed point of the PSOS surrounded by near-integrable tori. Based on transition state theory and a Floquet analysis of a periodic TS trajectory we compute the rate constant of the reaction with significantly reduced numerical effort compared to the propagation of a large trajectory ensemble.

Publication Types