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<p>Standard numerical solvers struggle with the long-term simulation of nonlinear Hamiltonian systems, often failing to preserve geometric structure and introducing unphysical errors. This paper introduces the symplectic physics-informed neural network integrator (SPINI), a novel two-stage hybrid algorithm. First, an unsupervised physics-informed neural network (PINN) learns the system’s Hamiltonian directly from its governing equations, requiring no trajectory data. Second, this learned Hamiltonian surrogate is embedded within a 4th-order Yoshida symplectic integrator to ensure a structure-preserving time evolution. We apply SPINI to the classical nonlinear pendulum and its parametric perturbation. Validations against the analytical solution and a standard Runge-Kutta solver (ode45) demonstrate SPINI’s superior accuracy and long-term fidelity, particularly in the strongly nonlinear, large-angle regime. SPINI offers a robust, law-driven framework for complex computational dynamics.</p>

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SPINI: a structure-preserving neural integrator for hamiltonian dynamics and parametric perturbation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月15日

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  • Chengtian Liang,
  • Xintong Wen,
  • Zhaoyu Zhu,
  • Lijiong Shen,
  • Yu Wang

摘要

Standard numerical solvers struggle with the long-term simulation of nonlinear Hamiltonian systems, often failing to preserve geometric structure and introducing unphysical errors. This paper introduces the symplectic physics-informed neural network integrator (SPINI), a novel two-stage hybrid algorithm. First, an unsupervised physics-informed neural network (PINN) learns the system’s Hamiltonian directly from its governing equations, requiring no trajectory data. Second, this learned Hamiltonian surrogate is embedded within a 4th-order Yoshida symplectic integrator to ensure a structure-preserving time evolution. We apply SPINI to the classical nonlinear pendulum and its parametric perturbation. Validations against the analytical solution and a standard Runge-Kutta solver (ode45) demonstrate SPINI’s superior accuracy and long-term fidelity, particularly in the strongly nonlinear, large-angle regime. SPINI offers a robust, law-driven framework for complex computational dynamics.