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A Data-Driven Koopman-Behavioral Distance for Nonlinear Dynamical Systems

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.06875

Authors: Sutavani, Sarang, Vaidya, Umesh

Institution: Clemson University

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation

Award: Scalable Approach to Optimal Control Design for Large-dimensional Systems Using Operator Theoretic Methods

OpenAlex ID: W7212071074

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