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New CW-EDMD method improves Koopman operator approximation for complex systems · 2 sources tracked

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Researchers have developed Cluster-Weighted Extended Dynamic Mode Decomposition (CW-EDMD), a novel method for approximating Koopman operators from data. This approach addresses the inefficiency of single global operators in systems with distinct local dynamics by learning a soft phase-space partition and a per-cluster operator. CW-EDMD utilizes an Expectation-Maximization objective that considers both geometric proximity and prediction residuals, allowing clusters to specialize where local Koopman models are accurate. Experiments on Lorenz, damped pendulum, and Duffing systems demonstrated significant error reductions compared to matched-degree EDMD, with median one-step error reductions of 57x, 2.7x, and 12x respectively. AI

IMPACT This method could enhance the modeling of complex systems with localized dynamics, potentially improving predictive capabilities in various scientific and engineering fields.

RANK_REASON The cluster contains a research paper detailing a new method for approximating Koopman operators.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

New CW-EDMD method improves Koopman operator approximation for complex systems · 2 sources tracked

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The cluster contains a research paper detailing a new method for approximating Koopman operators.
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COVERAGE [3]

  1. Hugging Face Daily Papers TIER_1 English(EN) ·

    Cluster-Weighted EDMD

    Extended Dynamic Mode Decomposition (EDMD) approximates Koopman operators from data, but a single global operator is inefficient when different state-space regions exhibit distinct local dynamics. We introduce Cluster-Weighted EDMD (CW-EDMD), which jointly learns a soft phase-spa…

  2. arXiv stat.ML TIER_1 English(EN) · Lorenzo Tomaz, Judd Rosenblatt, Flavio Kicis, Thomas B. Jones, Diogo Schwerz de Lucena ·

    Cluster-Weighted EDMD

    arXiv:2607.12243v1 Announce Type: cross Abstract: Extended Dynamic Mode Decomposition (EDMD) approximates Koopman operators from data, but a single global operator is inefficient when different state-space regions exhibit distinct local dynamics. We introduce Cluster-Weighted EDM…

  3. arXiv stat.ML TIER_1 English(EN) · Diogo Schwerz de Lucena ·

    Cluster-Weighted EDMD

    Extended Dynamic Mode Decomposition (EDMD) approximates Koopman operators from data, but a single global operator is inefficient when different state-space regions exhibit distinct local dynamics. We introduce Cluster-Weighted EDMD (CW-EDMD), which jointly learns a soft phase-spa…

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