719 citations · 1.9k across the 57 of their papers we have counts for
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Sparse Time Frequency Representations and Dynamical Systems
T. Y. Hou, Z. Shi, P. Tavallali
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations…
On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations
Thomas Y. Hou, Guo Luo
We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can be viewed as a local approximation to the Euler equations near the solid boundar…
Sparse Time-Frequency decomposition by dictionary learning
Thomas Y. Hou, Zuoqiang Shi
In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optim…
Potentially Singular Solutions of the 3D Incompressible Euler Equations
Guo Luo, Thomas Y. Hou
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynami…
Convergence of a data-driven time-frequency analysis method
Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali
In a recent paper, Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation…
Generalized Multiscale Finite Element Methods (GMsFEM)
Yalchin Efendiev, Juan Galvis, Thomas Y. Hou
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separatio…