Variational Continuation for Double Pendulum Periodic Orbits
We present a Hessian-based approach to numerically continue periodic orbits in dynamical systems. A loop (periodic orbit candidate) is parametrized as a Fourier series; a loss function is defined based on the deviation of the loop from the physical differential equations. Unlike previous work relying on hand-derived Jacobians, our method automates the process by leveraging automatic differentiation, a common machine learning technique. The continuation direction can be determined by the flat directions of the loss landscapes (directions with zero eigenvalues), making the search of periodic orbits efficient and guided. Our method is integrator-free, precisely initializes oscillations aroun...
| Authors | Leo Yao, Ziming Liu, Max Tegmark |
|---|---|
| Primary category | cs.LG |
| Published | 4 September 2026 |
| Last updated at source | 4 September 2026 |
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