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New framework models nonlinear delay dynamics using Koopman operator

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a novel framework for approximating the Koopman operator of nonlinear delay differential equations (DDEs). This approach bridges the gap between infinite-dimensional DDE dynamics and finite-dimensional Koopman learning by employing history discretization and a kernel-based reconstruction operator. The method, utilizing kernel-based extended dynamic mode decomposition (kEDMD), provides deterministic error bounds for predictions, separating the error into contributions from discretization, kernel interpolation, and regression. Numerical experiments confirm the framework's ability to reliably predict nonlinear delay systems, suggesting potential applications in future control systems. AI

IMPACT This research offers a novel method for modeling complex dynamic systems, potentially advancing control applications and scientific modeling.

RANK_REASON The cluster contains an academic paper detailing a new theoretical framework and method for modeling complex systems. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv cs.LG →

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New framework models nonlinear delay dynamics using Koopman operator

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The cluster contains an academic paper detailing a new theoretical framework and method for modeling complex systems. [lever_c_demoted from research: ic=1 ai=0.7]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Santosh Mohan Rajkumar, Dibyasri Barman, Kumar Vikram Singh, Debdipta Goswami ·

    On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations

    arXiv:2604.03086v2 Announce Type: replace-cross Abstract: This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for or…

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