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April 27, 2026PAMMOpen Access

Time‐Adaptive HénonNets for Separable Hamiltonian Systems

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Authors

KJKonrad JanikPBPeter Benner

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Overview

Randomized trial investigates time-adaptive symplectic integrators in Hamiltonian systems, suggesting improvements in irregular data sampling.

Key Points

  • This work aims to extend HénonNets to create time-adaptive symplectic integrators for Hamiltonian systems.
  • Introduction of a novel neural network architecture called T-HénonNets that can handle adaptive time steps.
  • Extension of T-HénonNets to non-autonomous Hamiltonian systems.
  • Numerical experiments performed to investigate theoretical approximation capabilities.
  • T-HénonNets exhibit effective performance in learning separable Hamiltonian systems with adaptive time steps.
  • Universal approximation theorems established for both T-HénonNets and TSympNets.
  • Challenges in applying the proposed methods to non-separable Hamiltonian systems highlighted.

Cite This Study

Janik et al. (2026) studied this question.

synapsesocial.com/papers/69eefdd1fede9185760d494chttps://doi.org/10.1002/pamm.70133
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