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Scientific Achievement

Developed a novel invertible architecture, the HenonNet, for predicting Poincaré maps efficiently for Hamiltonian systems.

Fast neural Poincaré maps for toroidal magnetic fields

Significance and Impact

Poincare maps reveal vital information about the confinement properties of Tokamaks.
Computing these maps are exceptionally expensive using classical numerical methods.
By leveraging knowledge of the fact that these maps preserve the symplectic form, fast neural predictions can be obtained.

RAPIDS: R. Maulik�TDS: J. Burby, X. Tang (LANL)

Research Details

The HénonNet was constructed by using Hénon’s Map which exactly preserves symplecticity.
The novel architecture was superior to comparable symplectic form preserving architectures.
Rich information from Poincaré maps were obtained in an expensive manner given small amounts of training data.

Burby, J., Tang, X., and Maulik, R., 2021. Fast neural Poincaré maps for toroidal magnetic fields, Plasma Phys. Control. Fusion 63 024001.

Learned flow for a simple Hamiltonian (the pendulum, above) and a complex Hamiltonian (representative of Tokamak dynamics, right) generated by HénonNet.

The novel Hénon layer composed of 4 Hénon maps

Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. This structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.

Contact: Romit Maulik – rmaulik@anl.gov

Link: https://iopscience.iop.org/article/10.1088/1361-6587/abcbaa/meta