Analysis of Fluid Flows via Spectral Properties of the Koopman Operator

2013

449 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

Citations in the corpus

• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, neutral): “…behavior [11], automated inference of dynamics [12, 13, 14], normal form identification in climate [15], nonlinear Laplacian spectral analysis [16], modeling emergent behavior [11], Koopman analysis [17, 18, 19, 20], automated inference of dynamics [12, 13, 14], and symbolic regression [21, 22].”
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, neutral): “Recent advances in the extended DMD have developed rigorous connections between DMD built on nonlinear observable functions and the Koopman operator theory for nonlinear dynamical systems [21, 23].”
• Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control (2015, unknown): “In fact, it is possible to establish topological conjugacy of the entire basin of attraction of a stable or unstable fixed point or periodic orbit with an associated linear system through the Koopman operator, as shown in [8, 10].”
• Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems (2017, unknown): “For a more detailed exposition on the relationships between spectral stability of a data-driven Koopman operator and that of the underlying system, we refer the reader to [28], [29].”
• Modal Analysis of Fluid Flows: Applications and Outlook (2019, unknown): “[4,5], dynamicmode decomposition (DMD) [6–9], Koopman analysis [7,10], global stability analysis [11,12], and resolvent analysis [13,14].”
• Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, unknown): “[77] I.”
• SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, unknown): “, system identification) is a rapidly developing field [1], with a range of techniques including classic linear approaches [2, 3], dynamic mode decomposition (DMD) [4, 5] and Koopman theory [6–9], nonlinear autoregressive models [10, 11], neural networks [12–20], Gaussian process regression [21, 22]”
• Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers (2016, unknown): “Another example of a data decomposition technique is Koopman [8,12] or dynamic mode [16] decomposition.”
• Variational Approach for Learning Markov Processes from Time Series Data (2017, unknown): “Examples include molecular dynamics [9,48], wireless communications [26,32] and fluid dynamics [37,15].”