Thomas Y. Hou

According to our database, Thomas Y. Hou authored at least 75 papers between 1991 and 2024.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of three.

2024

On the expressiveness and spectral bias of KANs.

Yixuan Wang, Jonathan W. Siegel, Ziming Liu, Thomas Y. Hou

CoRR, 2024

Nearly self-similar blowup of generalized axisymmetric Navier-Stokes and Boussinesq equations.

Thomas Y. Hou

CoRR, 2024

KAN: Kolmogorov-Arnold Networks.

Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljacic, Thomas Y. Hou, Max Tegmark

CoRR, 2024

2023

Potentially Singular Behavior of the 3D Navier-Stokes Equations.

Thomas Y. Hou

Found. Comput. Math., December, 2023

Potential Singularity of the 3D Euler Equations in the Interior Domain.

Thomas Y. Hou

Found. Comput. Math., December, 2023

Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations.

Yifan Chen, Thomas Y. Hou, Yixuan Wang

Multiscale Model. Simul., September, 2023

Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients.

Thomas Y. Hou, De Huang

Multiscale Model. Simul., March, 2023

Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics.

Jiajie Chen, Thomas Y. Hou

CoRR, 2023

2022

Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data.

Yifan Chen, Thomas Y. Hou

Multiscale Model. Simul., 2022

Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case.

Thomas Y. Hou, Shumao Zhang

CoRR, 2022

Exponentially Convergent Multiscale Finite Element Method.

Yifan Chen, Thomas Y. Hou, Yixuan Wang

CoRR, 2022

Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators.

Haydn Maust, Zongyi Li, Yixuan Wang, Daniel V. Leibovici, Oscar P. Bruno, Thomas Y. Hou, Anima Anandkumar

CoRR, 2022

2021

Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions.

Yifan Chen, Thomas Y. Hou, Yixuan Wang

Multiscale Model. Simul., 2021

Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold.

Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang

CoRR, 2021

The nearly singular behavior of the 3D Navier-Stokes equations.

Thomas Y. Hou

CoRR, 2021

Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations.

Yifan Chen, Thomas Y. Hou, Yixuan Wang

CoRR, 2021

Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients.

Thomas Y. Hou, De Huang

CoRR, 2021

Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference.

Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou

Proceedings of the 38th International Conference on Machine Learning, 2021

2020

Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization.

Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang

SIAM J. Math. Data Sci., 2020

Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization.

Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang

CoRR, 2020

Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data.

Yifan Chen, Thomas Y. Hou

CoRR, 2020

2019

Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study.

Guo Luo, Thomas Y. Hou

SIAM Rev., 2019

A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach.

Thomas Y. Hou, Dingjiong Ma, Zhiwen Zhang

Multiscale Model. Simul., 2019

A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition.

Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang

Multiscale Model. Simul., 2019

The subsampled Poincar\' e inequality for functional recovery.

Yifan Chen, Thomas Y. Hou

CoRR, 2019

A class of robust numerical methods for solving dynamical systems with multiple time scales.

Thomas Y. Hou, Zhongjian Wang, Zhiwen Zhang

CoRR, 2019

2018

An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition.

Thomas Y. Hou, De Huang, Ka Chun Lam, Pengchuan Zhang

Multiscale Model. Simul., 2018

Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow.

Thomas Y. Hou, Tianling Jin, Pengfei Liu

J. Nonlinear Sci., 2018

2017

Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs.

Thomas Y. Hou, Qin Li, Pengchuan Zhang

Multiscale Model. Simul., 2017

A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices.

Thomas Y. Hou, Qin Li, Pengchuan Zhang

Multiscale Model. Simul., 2017

An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients.

Thomas Y. Hou, Feng-Nan Hwang, Pengfei Liu, Chien-Chou Yao

J. Comput. Phys., 2017

Sparse Time-Frequency Decomposition for Multiple Signals with Same Frequencies.

Thomas Y. Hou, Zuoqiang Shi

Adv. Data Sci. Adapt. Anal., 2017

2016

An Accelerated Method for Nonlinear Elliptic PDE.

Hayden Schaeffer, Thomas Y. Hou

J. Sci. Comput., 2016

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods.

Eric T. Chung, Yalchin Efendiev, Thomas Y. Hou

J. Comput. Phys., 2016

2015

A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients.

Zhiwen Zhang, Maolin Ci, Thomas Y. Hou

Multiscale Model. Simul., 2015

On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data.

Chunguang Liu, Zuoqiang Shi, Thomas Y. Hou

Multiscale Model. Simul., 2015

Sparse + low-energy decomposition for viscous conservation laws.

Thomas Y. Hou, Qin Li, Hayden Schaeffer

J. Comput. Phys., 2015

A heterogeneous stochastic FEM framework for elliptic PDEs.

Thomas Y. Hou, Pengfei Liu

J. Comput. Phys., 2015

Extracting a shape function for a signal with intra-wave frequency modulation.

Thomas Y. Hou, Zuoqiang Shi

CoRR, 2015

2014

Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method.

Peyman Tavallali, Thomas Y. Hou, Zuoqiang Shi

Multiscale Model. Simul., 2014

Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation.

Guo Luo, Thomas Y. Hou

Multiscale Model. Simul., 2014

2013

A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients.

Mulin Cheng, Thomas Y. Hou, Mike P. Yan, Zhiwen Zhang

SIAM/ASA J. Uncertain. Quantification, 2013

Multiscale modeling of incompressible turbulent flows.

Thomas Y. Hou, X. Hu, Faiza Hussain

J. Comput. Phys., 2013

Generalized multiscale finite element methods (GMsFEM).

Yalchin Efendiev, Juan Galvis, Thomas Y. Hou

J. Comput. Phys., 2013

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms.

Mulin Cheng, Thomas Y. Hou, Zhiwen Zhang

J. Comput. Phys., 2013

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations.

Mulin Cheng, Thomas Y. Hou, Zhiwen Zhang

J. Comput. Phys., 2013

Convergence of a data-driven time-frequency analysis method

Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali

CoRR, 2013

Sparse Time Frequency Representations and Dynamical Systems.

Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali

CoRR, 2013

Sparse Time-Frequency decomposition by adaptive basis pursuit.

Thomas Y. Hou, Zuoqiang Shi

CoRR, 2013

2011

Introduction.

Thomas Y. Hou, Xue-Cheng Tai

Adv. Data Sci. Adapt. Anal., 2011

Adaptive Data Analysis via Sparse Time-Frequency Representation.

Thomas Y. Hou, Zuoqiang Shi

Adv. Data Sci. Adapt. Anal., 2011

2009

A Variant of the EMD Method for Multi-Scale Data.

Thomas Y. Hou, Mike P. Yan, Zhaohua Wu

Adv. Data Sci. Adapt. Anal., 2009

2008

Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier-Stokes Equations.

Thomas Y. Hou, Danping Yang, Hongyu Ran

Multiscale Model. Simul., 2008

Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations.

Thomas Y. Hou, Zuoqiang Shi

J. Comput. Phys., 2008

An efficient semi-implicit immersed boundary method for the Navier-Stokes equations.

Thomas Y. Hou, Zuoqiang Shi

J. Comput. Phys., 2008

2007

Mathematical modeling and simulation of aquatic and aerial animal locomotion.

Thomas Y. Hou, Valentin G. Stredie, Theodore Yao-Tsu Wu

J. Comput. Phys., 2007

Computing nearly singular solutions using pseudo-spectral methods.

Thomas Y. Hou, Ruo Li

J. Comput. Phys., 2007

2006

Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models.

Yalchin Efendiev, Thomas Y. Hou, Wuan Luo

SIAM J. Sci. Comput., 2006

On Global Well-Posedness of the Lagrangian Averaged Euler Equations.

Thomas Y. Hou, Congming Li

SIAM J. Math. Anal., 2006

A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media.

Thomas Y. Hou, Andrew Westhead, Danping Yang

Multiscale Model. Simul., 2006

Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations.

Thomas Y. Hou, Ruo Li

J. Nonlinear Sci., 2006

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations.

Shaoqiang Tang, Thomas Y. Hou, Wing Kam Liu

J. Comput. Phys., 2006

Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics.

Thomas Y. Hou, Wuan Luo, Boris Rozovskii, Haomin Zhou

J. Comput. Phys., 2006

Accurate multiscale finite element methods for two-phase flow simulations.

Yalchin Efendiev, Victor Ginting, Thomas Y. Hou, Richard E. Ewing

J. Comput. Phys., 2006

Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification.

Paul Dostert, Yalchin Efendiev, Thomas Y. Hou, Wuan Luo

J. Comput. Phys., 2006

2005

Special Section on Multiscale Modeling in Materials and Life Sciences.

Thomas Yizhao Hou, Petros Koumoutsakos

Multiscale Model. Simul., 2005

Special Issue on Multiscale Modeling in Biology.

Mark S. Alber, Thomas Yizhao Hou, James A. Glazier, Yi Jiang

Multiscale Model. Simul., 2005

2003

A mixed multiscale finite element method for elliptic problems with oscillating coefficients.

Zhiming Chen, Thomas Y. Hou

Math. Comput., 2003

2001

A new stabilizing technique for boundary integral methods for water waves.

Thomas Y. Hou, Pingwen Zhang

Math. Comput., 2001

2000

Convergence of a Nonconforming Multiscale Finite Element Method.

Yalchin R. Efendiev, Thomas Y. Hou, Xiao-hui Wu

SIAM J. Numer. Anal., 2000

1999

Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients.

Thomas Y. Hou, Xiao-hui Wu, Zhiqiang Cai

Math. Comput., 1999

Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering.

Russel E. Caflisch, Thomas Y. Hou, John S. Lowengrub

Math. Comput., 1999

1998

Convergence of a non-stiff boundary integral method for interfacial flows with surface tension.

Héctor D. Ceniceros, Thomas Y. Hou

Math. Comput., 1998

1993

The Convergence of an Exact Desingularization for Vortex Methods.

Thomas Y. Hou, John S. Lowengrub, Michael J. Shelley

SIAM J. Sci. Comput., 1993

1991

Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems.

Tony F. Chan, Thomas Y. Hou

SIAM J. Sci. Comput., 1991