Applied Koopman theory for partial differential equations and data-driven modeling of spatio-temporal systems
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Publication:1723113
DOI10.1155/2018/6010634zbMath1409.37029OpenAlexW2902132588MaRDI QIDQ1723113
J. Nathan Kutz, Steven L. Brunton, Joshua L. Proctor
Publication date: 19 February 2019
Published in: Complexity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2018/6010634
Computational learning theory (68Q32) NLS equations (nonlinear Schrödinger equations) (35Q55) Time series analysis of dynamical systems (37M10) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Ginzburg-Landau equations (35Q56)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- A kernel-based method for data-driven Koopman spectral analysis
- On the numerical approximation of the Perron-Frobenius and Koopman operator
- Data-driven model reduction and transfer operator approximation
- A data-driven approximation of the koopman operator: extending dynamic mode decomposition
- Kernel methods in machine learning
- Non-linear autonomous systems of differential equations and Carleman linearization procedure
- Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes
- Dynamic data-driven reduced-order models
- Comparison of systems with complex behavior
- Spectral properties of dynamical systems, model reduction and decompositions
- On dynamic mode decomposition: theory and applications
- Sparse Sensor Placement Optimization for Classification
- Challenges in Climate Science and Contemporary Applied Mathematics
- Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems
- Applied Koopmanism
- Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
- Dynamic mode decomposition of numerical and experimental data
- Mode‐Locked Soliton Lasers
- Cluster-based reduced-order modelling of a mixing layer
- Spectral analysis of nonlinear flows
- Infinite-dimensional Carleman linearization, the Lie series and optimal control of non-linear partial differential equations
- Hamiltonian Systems and Transformation in Hilbert Space
- Dynamical Systems of Continuous Spectra
- Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
- Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows
- A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
- Approximation of Large-Scale Dynamical Systems
- The partial differential equation ut + uux = μxx
- On a quasi-linear parabolic equation occurring in aerodynamics