Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems

2025/06/21 by van Goor, Pieter, Mahony, Robert, Schaller, Manuel +1 · 2 citations
#Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2506.17817

Abstract

Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is invariant under the Koopman operator. In data-driven approximation such as Extended Dynamic Mode Decomposition, this invariance is typically lost due to the presence of (finite-data) approximation errors. In this work, we show that reprojections are crucial for reliable predictions. We provide an approach via closest-point projections that ensure consistency with this nonlinear manifold, which is strongly related to a Riemannian metric and maximum likelihood estimates. While these results are already novel for autonomous systems, we present our approach for parametric systems, providing the basis for data-driven bifurcation analysis and control applications.

Citations

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Cited by

• An overview of Koopman-based control: From error bounds to closed-loop guarantees
• Learning Koopman Models From Data Under General Noise Conditions

Related

• Reprojection methods for Koopman-based modelling and prediction
• Modern Koopman Theory for Dynamical Systems
• Modern Koopman Theory for Dynamical Systems
• Nonlinear Data-Driven Approximation of the Koopman Operator
• An overview of Koopman-based control: From error bounds to closed-loop guarantees