1.9k citations · 5.7k across the 37 of their papers we have counts for
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Identifying Finite-Time Coherent Sets from Limited Quantities of Lagrangian Data
Matthew O. Williams, Irina I. Rypina, Clarence W. Rowley
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions stat…
Data Fusion via Intrinsic Dynamic Variables: An Application of Data-Driven Koopman Spectral Analysis
Matthew O. Williams, Clarence W. Rowley, Igor Mezić +1
We demonstrate that numerically computed approximations of Koopman eigenfunctions and eigenvalues create a natural framework for data fusion in applications governed by nonlinear e…
Uncertainty Quantification for Airfoil Icing using Polynomial Chaos Expansions
Anthony M. DeGennaro, Clarence W. Rowley, Luigi Martinelli
The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncer…
A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis
Matthew O. Williams, Clarence W. Rowley, Ioannis G. Kevrekidis
A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This ap…
A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
Matthew O. Williams, Ioannis G. Kevrekidis, Clarence W. Rowley
The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, an…
Dynamic Mode Decomposition for Large and Streaming Datasets
Maziar S. Hemati, Matthew O. Williams, Clarence W. Rowley
We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical inform…