Hou, Thomas Y.
(2022)
Potential Singularity of the 3D Euler Equations in the Interior Domain
Foundations of Computational Mathematics;
(In Press)
Hou, Thomas Y.
(2022)
Potentially Singular Behavior of the 3D Navier-Stokes Equations
Foundations of Computational Mathematics;
(In Press)
Chen, Yifan; Hou, Thomas Y.
(2022)
Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data
Multiscale Modeling and Simulation;
Vol.
20;
No.
1;
Zhang, Shumao; Zhang, Pengchuan et al.
(2021)
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference
Proceedings of Machine Learning Research;
Vol.
139;
38th International Conference on Machine Learning, 18-24 July 2021
, [Online Only]
Chen, Yifan; Hou, Thomas Y. et al.
(2021)
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions
Multiscale Modeling and Simulation;
Vol.
19;
No.
2;
Chen, Jiajie; Hou, Thomas Y. et al.
(2021)
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations
Communications on Pure and Applied Mathematics;
Vol.
74;
No.
6;
Chen, Jiajie; Hou, Thomas Y.
(2021)
Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^(1,α) Velocity and Boundary
Communications in Mathematical Physics;
Vol.
383;
No.
3;
Chen, Yifan; Hou, Thomas Y.
(2021)
Function approximation via the subsampled Poincaré inequality
Discrete and Continuous Dynamical Systems - Series A;
Vol.
41;
No.
1;
Chen, Jiajie; Hou, Anthony et al.
(2020)
A prototype knockoff filter for group selection with FDR control
Information and Inference;
Vol.
9;
No.
2;
Zhang, Zhiwen; Rosakis, Phoebus et al.
(2020)
A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates
Journal of the Royal Society Interface;
Vol.
17;
No.
166;
Hou, Thomas Y.; Lam, Ka Chun et al.
(2019)
Solving Bayesian inverse problems from the perspective of deep generative networks
Computational Mechanics;
Vol.
64;
No.
2;
Chen, Jiajie; Hou, Anthony et al.
(2019)
A pseudo knockoff filter for correlated features
Information and Inference;
Vol.
8;
No.
2;
Hou, Thomas Y.; Jin, Tianling et al.
(2018)
Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow
Journal of Nonlinear Science;
Vol.
28;
No.
6;
Hou, Thomas Y.; Zhang, Pengchuan
(2017)
Sparse operator compression of higher-order elliptic operators with rough coefficients
Research in the Mathematical Sciences;
Vol.
4;
No.
1;
Choi, Kyudong; Hou, Thomas Y. et al.
(2017)
On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations
Communications on Pure and Applied Mathematics;
Vol.
70;
No.
11;
Liu, ChunGuang; Shi, ZuoQiang et al.
(2017)
A two-level method for sparse time-frequency representation of multiscale data
Science China Mathematics;
Vol.
60;
No.
10;
Hou, Thomas Y.; Li, Qin et al.
(2017)
Exploring the locally low dimensional structure in solving random elliptic PDEs
Multiscale Modeling & Simulation;
Vol.
15;
No.
2;
Hou, Thomas Y.; Li, Qin et al.
(2017)
A sparse decomposition of low rank symmetric positive semi-definite matrices
Multiscale Modeling and Simulation;
Vol.
15;
No.
1;
Schaeffer, Hayden; Hou, Thomas Y.
(2016)
An Accelerated Method for Nonlinear Elliptic PDE
Journal of Scientific Computing;
Vol.
69;
No.
2;
Chung, Eric; Efendiev, Yalchin et al.
(2016)
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
Journal of Computational Physics;
Vol.
320;
Hou, Thomas Y.; Liu, Pengfei
(2016)
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient
Discrete and Continuous Dynamical Systems;
Vol.
36;
No.
8;
Huang, Norden E.; Daubechies, Ingrid et al.
(2016)
Adaptive data analysis: theory and applications
Philosophical Transactions A: Mathematical, Physical and Engineering Sciences;
Vol.
374;
No.
2065;
Hou, Thomas Y.; Shi, Zuoqiang
(2016)
Extracting a shape function for a signal with intra-wave frequency modulation
Philosophical Transactions A: Mathematical, Physical and Engineering Sciences;
Vol.
374;
No.
2065;
Hou, Thomas Y.; Shi, Zuoqiang
(2016)
Sparse time-frequency decomposition based on dictionary adaptation
Philosophical Transactions A: Mathematical, Physical and Engineering Sciences;
Vol.
374;
No.
2065;
Hou, Thomas Y.; Liu, Pengfei et al.
(2016)
A Model Reduction Method for Elliptic PDEs with Random Input Using the Heterogeneous Stochastic FEM Framework
Bulletin of the Intitute of Mathematics Academia Sinica;
Vol.
11;
No.
1;
Tavallali, Peyman; Hou, Thomas Y. et al.
(2015)
On the convergence and accuracy of the cardiovascular intrinsic frequency method
Royal Society Open Science;
Vol.
2;
No.
12;
Liu, Chunguang; Shi, Zuoqiang et al.
(2015)
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data
Multiscale Modeling and Simulation;
Vol.
13;
No.
3;
Zhang, Zhiwen; Ci, Maolin et al.
(2015)
A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients
Multiscale Modeling and Simulation;
Vol.
13;
No.
1;
Hou, Thomas Y.; Liu, Pengfei
(2015)
A heterogeneous stochastic FEM framework for elliptic PDEs
Journal of Computational Physics;
Vol.
281;
Hou, Thomas Y.; Shi, Zuoqiang et al.
(2015)
Sparse Time Frequency Representations and Dynamical Systems
Communications in Mathematical Sciences;
Vol.
13;
No.
3;
Tavallali, Peyman; Hou, Thomas Y. et al.
(2014)
Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method
Multiscale Modeling and Simulation;
Vol.
12;
No.
4;
Luo, Guo; Hou, Thomas Y.
(2014)
Potentially singular solutions of the 3D axisymmetric Euler equations
Proceedings of the National Academy of Sciences of the United States of America;
Vol.
111;
No.
36;
Zhang, Zhiwen; Hu, Xin et al.
(2014)
Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient
Communications in Computational Physics;
Vol.
16;
No.
3;
Hou, Thomas Y.; Shi, Zuoqiang et al.
(2014)
Convergence of a data-driven time–frequency analysis method
Applied and Computational Harmonic Analysis;
Vol.
37;
No.
2;
Pahlevan, Niema M.; Tavallali, Peyman et al.
(2014)
Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications
Journal of the Royal Society Interface;
Vol.
11;
No.
98;
Hou, Thomas Y.; Lei, Zhen et al.
(2014)
On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations
Archive for Rational Mechanics and Analysis;
Vol.
212;
No.
2;
Ci, Maolin; Hou, Thomas Y. et al.
(2014)
A Multiscale Model Reduction Method for Partial Differential Equations
ESAIM-Mathematical Modelling and Numerical Analysis;
Vol.
48;
No.
2;
Hou, Thomas Yizhao; Shi, Zuoqiang
(2013)
Sparse time-frequency representation of nonlinear and nonstationary data
Science China Mathematics;
Vol.
56;
No.
12;
Efendiev, Yalchin; Galvis, Juan et al.
(2013)
Generalized multiscale finite element methods (GMsFEM)
Journal of Computational Physics;
Vol.
251;
Hou, Thomas Y.; Shi, Zuoqiang
(2013)
Data-driven time–frequency analysis
Applied and Computational Harmonic Analysis;
Vol.
35;
No.
2;
Hou, T. Y.; Hu, X. et al.
(2013)
Multiscale modeling of incompressible turbulent flows
Journal of Computational Physics;
Vol.
232;
No.
1;
Miller, Cass T.; Dawson, Clint N. et al.
(2013)
Numerical simulation of water resources problems: Models, methods, and trends
Advances in Water Resources;
Vol.
51;
Hou, Thomas Y.; Shi, Zuoqiang et al.
(2012)
On singularity formation of a 3D model for incompressible Navier–Stokes equations
Advances in Mathematics;
Vol.
230;
No.
2;
Hou, Thomas Y.; Shi, Zuoqiang
(2011)
Adaptive data analysis via sparse time-frequency representation
Advances in Adaptive Data Analysis;
Vol.
3;
No.
1-2;
Hou, Thomas Y.; Tai, Xue-Cheng
(2011)
Introduction
Advances in Adaptive Data Analysis;
Vol.
3;
No.
1-2;
Sparse Representation of Multiscale Data and Images: Theory and Applications, 14-17 December 2009
, Singapore
Hou, Thomas Y.; Li, Congming et al.
(2011)
On Singularity Formation of a Nonlinear Nonlocal System
Archive for Rational Mechanics and Analysis;
Vol.
199;
No.
1;
Hou, Thomas Y.; Tai, Xue-Cheng
(2011)
Introduction
Advances in Adaptive Data Analysis;
Vol.
3;
No.
1-2;
Chu, C.-C.; Graham, I. G. et al.
(2010)
A new multiscale finite element method for high-contrast elliptic interface problems
Mathematics of Computation;
Vol.
79;
No.
272;
Hou, Thomas Y.; Lei, Zhen
(2009)
On the Partial Regularity of a 3D Model of the Navier-Stokes Equations
Communications in Mathematical Physics;
Vol.
287;
No.
2;
Hou, Thomas Y.; Lei, Zhen
(2009)
On the stabilizing effect of convection in three-dimensional incompressible flows
Communications on Pure and Applied Mathematics;
Vol.
62;
No.
4;
Hou, Thomas Y.; Liang, Dong
(2009)
Multiscale analysis for convection dominated transport equations
Discrete and Continuous Dynamical Systems;
Vol.
23;
No.
1-2;
Hou, Thomas Y.; Wetton, Brian R.
(2009)
Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries
Journal of Computational Mathematics;
Vol.
27;
No.
4;
Hou, Thomas Y.; Lei, Zhen et al.
(2008)
Global Regularity of the 3D Axi-symmetric
Navier-Stokes Equations with Anisotropic Data
Communications in Partial Differential Equation;
Vol.
33;
No.
9;
Efendiev, Y.; Hou, T. et al.
(2008)
Multiscale simulations of porous media flows in flow-based coordinate system
Computational Geosciences;
Vol.
12;
No.
3;
Hou, Thomas Y.; Li, Congming
(2008)
Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl
Communications on Pure and Applied Mathematics;
Vol.
61;
No.
5;
Hou, Thomas Y.; Li, Ruo
(2007)
Computing nearly singular solutions using pseudo-spectral methods
Journal of Computational Physics;
Vol.
226;
No.
1;
Hou, T. Y.; Stredie, V. G. et al.
(2007)
Mathematical modeling and simulation of aquatic and aerial animal locomotion
Journal of Computational Physics;
Vol.
225;
No.
2;
Efendiev, Y.; Hou, T. Y.
(2007)
Multiscale finite element methods for porous media flows and their applications
Applied Numerical Mathematics;
Applied Numerical Mathematics;
Vol.
57;
No.
5-7;
International Conference on Scientific Computing, Jun. 04-08, 2005
, Nanjing Univ, Nanjing, China
Hou, Thomas Y.
(2007)
Organized structures, memory, and the decay of turbulence
Proceedings of the National Academy of Sciences of the United States of America;
Vol.
104;
No.
16;
Tang, Shao-Qiang; Liu, Wing K. et al.
(2007)
Bridging Atomistic/Continuum Scales in Solids with Moving Dislocations
Chinese Physics Letters;
Vol.
24;
No.
1;
Hou, Thomas Y.; Westhead, Andrew et al.
(2006)
A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media
Multiscale Modeling & Simulation;
Vol.
5;
No.
4;
Hou, Thomas Y.; Li, Congming
(2006)
On Global Well-Posedness of the Lagrangian Averaged Euler Equations
SIAM Journal on Mathematical Analysis;
Vol.
38;
No.
3;
Hou, T. Y.; Stredie, V. G. et al.
(2006)
A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate
Communications in Computational Physics;
Vol.
1;
No.
2;
Deng, Jian; Hou, Thomas Y. et al.
(2006)
Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation
Communications in Partial Differential Equations;
Vol.
31;
No.
2;
Efendiev, Y.; Hou, T. et al.
(2006)
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
SIAM Journal on Scientific Computing;
Vol.
28;
No.
2;
Hou, Thomas Y.; Yang, Danping et al.
(2005)
Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation
Discrete and Continuous Dynamical Systems;
Vol.
13;
No.
5;
Hou, Thomas Y.
(2005)
Multiscale modelling and computation of fluid flow
International Journal for Numerical Methods in Fluids;
Vol.
47;
No.
8-9;
8th ICFD Conference on Numerical Methods for Fluid Dynamics, 20-30 March 2005
, Oxford, England
Deng, Jian; Hou, Thomas Y. et al.
(2005)
Geometric Properties and Nonblowup of 3D Incompressible Euler Flow
Communications in Partial Differential Equations;
Vol.
30;
No.
1-2;
Fetecau, R. C.; Hou, T. Y.
(2004)
A modified particle method for semilinear hyperbolic systems with oscillatory solutions
Methods and Applications of Analysis;
Vol.
11;
No.
4;
Efendiev, Y.; Hou, T. Y. et al.
(2004)
Multiscale Finite Element Methods for Nonlinear Problems and their Applications
Communications in Mathematical Sciences;
Vol.
2;
No.
4;
Hou, Thomas Y.; Yang, Dan-ping et al.
(2004)
Homogenization of incompressible Euler equations
Journal of Computational Mathematics;
Vol.
22;
No.
2;
Hou, Thomas Y.; Hu, Gang et al.
(2003)
Singularity formation in three-dimensional vortex sheets
Physics of Fluids;
Vol.
15;
No.
1;
Aarnes, Jørg; Hou, Thomas Y.
(2002)
Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios
Acta Mathematicae Applicatae Sinica, English Series;
Vol.
18;
No.
1;
Ceniceros, Hector D.; Hou, Thomas Y.
(2000)
The singular perturbation of surface tension in Hele-Shaw flows
Journal of Fluid Mechanics;
Vol.
409;
Efendiev, Yalchin R.; Hou, Thomas Y. et al.
(2000)
Convergence of a nonconforming multiscale finite element method
SIAM Journal on Numerical Analysis;
Vol.
37;
No.
3;
Ceniceros, Hector D.; Hou, Thomas Y. et al.
(1999)
Numerical study of Hele-Shaw flow with suction
Physics of Fluids;
Vol.
11;
No.
9;
Ceniceros, Hector D.; Hou, Thomas Y.
(1999)
Dynamic generation of capillary waves
Physics of Fluids;
Vol.
11;
No.
5;
Hou, Thomas Yizhao
(1998)
Numerical Study of Free Interface Problems Using Boundary Integral Methods
Documenta Mathematica;
Vol.
Extra ;
No.
Volume;
Beale, J. Thomas; Hou, Thomas Y. et al.
(1996)
Convergence of a Boundary Integral Method for Water Waves
SIAM Journal on Numerical Analysis;
Vol.
33;
No.
5;