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arXiv · 2506.17817

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

Pieter van Goor·Robert Mahony·Manuel Schaller·Karl Worthmann
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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.

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Pieter van Goor, Robert Mahony, Manuel Schaller, Karl Worthmann. 2025-06-21. Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems. https://arxiv.org/abs/2506.17817

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