75 citations · 161 across the 11 of their papers we have counts for
5 papers · 1 filter
Robust and scalable methods for the dynamic mode decomposition
Travis Askham, Peng Zheng, Aleksandr Aravkin +1
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a mat…
Stability and Dynamics of Microring Combs: Elliptic function solutions of the Lugiato-Lefever equation
Chang Sun, Travis Askham, J. Nathan Kutz
We consider a new class of periodic solutions to the Lugiato-Lefever equations (LLE) that govern the electromagnetic field in a microresonator cavity. Specifically, we rigorously c…
A stabilized separation of variables method for the modified biharmonic equation
Travis Askham
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of…
Integral equation formulation of the biharmonic Dirichlet problem
Manas Rachh, Travis Askham
We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes proble…
Variable projection methods for an optimized dynamic mode decomposition
Travis Askham, J. Nathan Kutz
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models t…