A Data-Driven Koopman-Behavioral Distance for Nonlinear Dynamical Systems
Abstract
Comparing nonlinear dynamical systems directly from trajectory data remains challenging because finite-horizon trajectory representations are generally coordinate dependent. Motivated by recent behavioral subspace approaches for linear systems, this paper introduces a Koopman-behavioral distance for nonlinear stochastic systems using multi-rollout trajectory data. State measurements are lifted through a common observable dictionary, and dominant lifted behavioral subspaces are compared using Grassmannian distances without explicit Koopman operator identification. We establish coordinate invariance, connection with recently proposed linear behavioral distances under exact lifted closure, and robustness to approximate closure. Numerical examples demonstrate coordinate invariance and parameter discrimination.
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BibTeX
@misc{sutavani2026datadriven,
title = {{A Data-Driven Koopman-Behavioral Distance for Nonlinear Dynamical Systems}},
author = {Sarang Sutavani and Umesh Vaidya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06875},
eprint = {2609.06875},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06875},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Data-Driven Koopman-Behavioral Distance for Nonlinear Dynamical Systems
AU - Sarang Sutavani
AU - Umesh Vaidya
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06875
UR - https://arxiv.org/abs/2609.06875
AB - Comparing nonlinear dynamical systems directly from trajectory data remains challenging because finite-horizon trajectory representations are generally coordinate dependent. Motivated by recent behavioral subspace approaches for linear systems, this paper introduces a Koopman-behavioral distance for nonlinear stochastic systems using multi-rollout trajectory data. State measurements are lifted through a common observable dictionary, and dominant lifted behavioral subspaces are compared using Grassmannian distances without explicit Koopman operator identification. We establish coordinate invariance, connection with recently proposed linear behavioral distances under exact lifted closure, and robustness to approximate closure. Numerical examples demonstrate coordinate invariance and parameter discrimination.
ER -