Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spec...

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Veröffentlicht in:Scientific reports Jg. 15; H. 1; S. 22127 - 13
Hauptverfasser: Nayak, Indranil, Chakrabarti, Ananda, Kumar, Mrinal, Teixeira, Fernando L., Goswami, Debdipta
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Nature Publishing Group UK 01.07.2025
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Electrical and electronic engineering
Engineering
Humanities and Social Sciences
Koopman
Machine learning
Mechanical engineering
multidisciplinary
Neural networks
Science
Science (multidisciplinary)
Neural networks
Machine learning
Koopman
ISSN:2045-2322, 2045-2322
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Zusammenfassung:Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.
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USDOE
National Science Foundation (NSF)/USDOE
SC0022982
None
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-025-05222-7