296 citations · 353 across the 4 of their papers we have counts for
6 papers
Numerical Diagnostics for Systems of Differential Algebraic Equations
Matthew O. Williams, Teems E. Lovett
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even…
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
Scott T. M. Dawson, Maziar S. Hemati, Matthew O. Williams +1
Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulnes…
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…
Coarse graining, dynamic renormalization and the kinetic theory of shock clustering
Xingjie Li, Matthew O. Williams, Ioannis G. Kevrekidis +1
We demonstrate the utility of the equation free methodology developed by one of the authors (I.G.K) for the study of scalar conservation laws with disordered initial conditions. Th…
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…