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About this paper
Simone Servadio, Giovanni Lavezzi, Christian Hofmann, Di Wu, Richard Linares
Koopman Operator State Transition Polynomial Maps are used to propagate complete probability density functions through deterministic, volume-preserving nonlinear dynamics. In a Duffing oscillator experiment, the inverse-map formulation reproduces the deformation of an initially Gaussian distribution with substantial agreement with a one-million-sample Monte Carlo reference and supports recursive prediction through polynomial reduction.
Key insights
- For Hamiltonian systems, phase-space volume preservation makes the density constant along trajectories, reducing PDF propagation to evaluation through the inverse solution flow.
- Reversing the Koopman propagation interval provides a direct approximate inverse of the polynomial flow map, avoiding a separate nonlinear map-inversion procedure.
- Galerkin Koopman models preserve the expected imaginary-axis eigenvalue structure more accurately than the tested EDMD model, whose finite-data approximation introduces small real components and larger long-horizon state errors.
Summary by alphaXiv.
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