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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Weighted Composition Operators for Learning Nonlinear Dynamics.

Benjamin P Russo1, Daniel A Messenger2, David Bortz2

  • 1Oak Ridge National Laboratory, Computer Science and Mathematics Division, Oak Ridge, TN 37830.

Ifac-Papersonline
|July 21, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces the weighted composition operator as a novel approach for analyzing dynamical systems. This method offers a data-driven alternative for modeling system dynamics, particularly when traditional Koopman operator methods are insufficient.

Keywords:
Machine Learning and ControlOperator Theoretic Methods in Systems TheorySystem Identification

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Area of Science:

  • Dynamical Systems
  • Operator Theory
  • Data Science

Background:

  • Operator theoretic methods, including Koopman operators, are prevalent in dynamical systems analysis.
  • These methods leverage invariant subspaces and eigenfunctions for linear system modeling.
  • Limitations exist when Koopman operators lack exploitable eigenfunctions.

Purpose of the Study:

  • To introduce the weighted composition operator as an alternative for dynamical systems study.
  • To address limitations of traditional Koopman operator methods.
  • To present a new data-driven algorithm for dynamical system analysis.

Main Methods:

  • Utilizing weighted composition operators, which are compact across various dynamics and spaces.
  • Interacting weighted composition operators with occupation kernels and vector-valued kernels.
  • Developing a novel algorithm for data-driven dynamical system modeling.

Main Results:

  • Weighted composition operators provide estimations of underlying system dynamics.
  • The proposed algorithm facilitates data-driven study of dynamical systems.
  • Numerical experiments demonstrate convergence, validating the approach as a proof of concept.

Conclusions:

  • The weighted composition operator offers a viable alternative for dynamical systems analysis.
  • This operator-based framework can be approximated even without ideal eigenfunctions.
  • The presented algorithm provides a new tool for data-driven modeling of complex systems.