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Symplectic Integrators & KAM Theory - Long-Time Hamiltonian Dynamics

  • Task ID: math.symplectic_integrators
  • Domain: math
  • Subdomain: numerical_odes_dynamical_systems
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: dynamics, numerical_methods, hamiltonian_systems, chaos

Runtime and requirements

  • Estimated time: 10-30 minutes
  • Python: >=3.9
  • Packages: numpy>=1.24.0, pandas>=2.0.0, matplotlib>=3.7.0, scipy>=1.11.0
  • GPU required: no
  • Network required: no

Public input and output contract

Inputs

  • initial_conditions.csv (data): Initial conditions for multiple orbits. Columns: orbit_id, x1, x2, x3, x4.
  • trajectory_obs.csv (data): Short noisy trajectory probes for system identification. Columns: t, probe_id, x1, x2, x3, x4.

Outputs

  • analysis.py (code): Python script that implements the integration and analysis.
  • energy_drift.csv (data): Energy drift over time. Columns: orbit_id, integrator, time, rel_energy_error, energy.
  • lyapunov_exponents.csv (data): Full Lyapunov spectrum. Columns: orbit_id, lambda_1, lambda_2, lambda_3, lambda_4, lambda_max.
  • poincare_points.csv (data): Poincare section points. Columns: orbit_id, q1, p1.
  • energy_drift.png (figure): Plot of relative energy error vs time.
  • poincare_section.png (figure): Plot of the Poincare section.

Public repository files

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Provenance

This task is included in the current seed42 benchmark set at dataset revision f11a199f71fb4b854ac43a1bf548d5df519141a9.

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