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TZID:Europe/Paris
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DTSTART:20260329T010000
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DTSTART;TZID=Europe/Paris:20260219T110000
DTEND;TZID=Europe/Paris:20260219T120000
DTSTAMP:20260519T055838
CREATED:20260213T133735Z
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UID:21023-1771498800-1771502400@www.math.ens.psl.eu
SUMMARY:Thibaut Germain : "A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems"
DESCRIPTION:The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition\, offering a natural framework for comparison. We propose a novel approach representing each system as a distribution of its joint operator eigenvalues and spectral projectors and defining a metric between systems leveraging optimal transport. The proposed metric is invariant to the sampling frequency of trajectories. It is also computationally efficient\, supported by finite-sample convergence guarantees\, and enables the computation of Fréchet means\, providing interpolation between dynamical systems. Experiments on simulated and real-world datasets show that our approach consistently outperforms standard operator-based distances in machine learning applications\, including dimensionality reduction and classification\, and provides meaningful interpolation between dynamical systems.
URL:https://www.math.ens.psl.eu/evenement/thibaut-germain-a-spectral-grassmann-wasserstein-metric-for-operator-representations-of-dynamical-systems/
LOCATION:Salle W
CATEGORIES:CSD seminar
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