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Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

Journal Article · · Scientific Reports
 [1];  [2];  [2]
  1. Univ. of California, San Diego, CA (United States)
  2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations
A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal U(1) symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal U(1) symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.
Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
89233218CNA000001; AC02-05CH11231
OSTI ID:
2426510
Report Number(s):
LA-UR--22-30516
Journal Information:
Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 13; ISSN 2045-2322
Publisher:
Nature Publishing GroupCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (6)

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