Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems. - Tony F. Chan; Thomas Y. Hou 001 (SIAM J. Sci. Comput., 1991)

The Convergence of an Exact Desingularization for Vortex Methods. - Thomas Y. Hou 001; John S. Lowengrub; Michael J. Shelley (SIAM J. Sci. Comput., 1993)

Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. - Héctor D. Ceniceros; Thomas Y. Hou 001 (Math. Comput., 1998)

Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. - Russel E. Caflisch; Thomas Y. Hou 001; John S. Lowengrub (Math. Comput., 1999)

Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. - Thomas Y. Hou 001; Xiao-hui Wu; Zhiqiang Cai 001 (Math. Comput., 1999)

Convergence of a Nonconforming Multiscale Finite Element Method. - Yalchin R. Efendiev; Thomas Y. Hou 001; Xiao-hui Wu (SIAM J. Numer. Anal., 2000)

A new stabilizing technique for boundary integral methods for water waves. - Thomas Y. Hou 001; Pingwen Zhang (Math. Comput., 2001)

A mixed multiscale finite element method for elliptic problems with oscillating coefficients. - Zhiming Chen; Thomas Y. Hou 001 (Math. Comput., 2003)

Special Issue on Multiscale Modeling in Biology. - Mark S. Alber; Thomas Yizhao Hou; James A. Glazier; Yi Jiang (Multiscale Model. Simul., 2005)

Special Section on Multiscale Modeling in Materials and Life Sciences. - Thomas Yizhao Hou; Petros Koumoutsakos (Multiscale Model. Simul., 2005)

Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. - Paul Dostert; Yalchin Efendiev; Thomas Y. Hou 001; Wuan Luo (J. Comput. Phys., 2006)

Accurate multiscale finite element methods for two-phase flow simulations. - Yalchin Efendiev; Victor Ginting; Thomas Y. Hou 001; Richard E. Ewing (J. Comput. Phys., 2006)

Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. - Thomas Y. Hou 001; Wuan Luo; Boris Rozovskii; Haomin Zhou 001 (J. Comput. Phys., 2006)

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations. - Shaoqiang Tang; Thomas Y. Hou 001; Wing Kam Liu (J. Comput. Phys., 2006)

Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations. - Thomas Y. Hou 001; Ruo Li (J. Nonlinear Sci., 2006)

A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media. - Thomas Y. Hou 001; Andrew Westhead; Danping Yang (Multiscale Model. Simul., 2006)

On Global Well-Posedness of the Lagrangian Averaged Euler Equations. - Thomas Y. Hou 001; Congming Li (SIAM J. Math. Anal., 2006)

Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models. - Yalchin Efendiev; Thomas Y. Hou 001; Wuan Luo (SIAM J. Sci. Comput., 2006)

Computing nearly singular solutions using pseudo-spectral methods. - Thomas Y. Hou 001; Ruo Li (J. Comput. Phys., 2007)

Mathematical modeling and simulation of aquatic and aerial animal locomotion. - Thomas Y. Hou 001; Valentin G. Stredie; Theodore Yao-Tsu Wu (J. Comput. Phys., 2007)

An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. - Thomas Y. Hou 001; Zuoqiang Shi (J. Comput. Phys., 2008)

Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. - Thomas Y. Hou 001; Zuoqiang Shi (J. Comput. Phys., 2008)

Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier-Stokes Equations. - Thomas Y. Hou 001; Danping Yang; Hongyu Ran (Multiscale Model. Simul., 2008)

A Variant of the EMD Method for Multi-Scale Data. - Thomas Y. Hou 001; Mike P. Yan; Zhaohua Wu (Adv. Data Sci. Adapt. Anal., 2009)

Adaptive Data Analysis via Sparse Time-Frequency Representation. - Thomas Y. Hou 001; Zuoqiang Shi (Adv. Data Sci. Adapt. Anal., 2011)

Introduction. - Thomas Y. Hou 001; Xue-Cheng Tai (Adv. Data Sci. Adapt. Anal., 2011)

Sparse Time-Frequency decomposition by adaptive basis pursuit. - Thomas Y. Hou 001; Zuoqiang Shi (CoRR, 2013)

Sparse Time Frequency Representations and Dynamical Systems. - Thomas Y. Hou 001; Zuoqiang Shi; Peyman Tavallali (CoRR, 2013)

Convergence of a data-driven time-frequency analysis method - Thomas Y. Hou 001; Zuoqiang Shi; Peyman Tavallali (CoRR, 2013)

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations. - Mulin Cheng; Thomas Y. Hou 001; Zhiwen Zhang 001 (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 001; Zhiwen Zhang 001 (J. Comput. Phys., 2013)

Generalized multiscale finite element methods (GMsFEM). - Yalchin Efendiev; Juan Galvis; Thomas Y. Hou 001 (J. Comput. Phys., 2013)

Multiscale modeling of incompressible turbulent flows. - Thomas Y. Hou 001; X. Hu; Faiza Hussain (J. Comput. Phys., 2013)

A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. - Mulin Cheng; Thomas Y. Hou 001; Mike P. Yan; Zhiwen Zhang 001 (SIAM/ASA J. Uncertain. Quantification, 2013)

Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation. - Guo Luo; Thomas Y. Hou 001 (Multiscale Model. Simul., 2014)

Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method. - Peyman Tavallali; Thomas Y. Hou 001; Zuoqiang Shi (Multiscale Model. Simul., 2014)

Extracting a shape function for a signal with intra-wave frequency modulation. - Thomas Y. Hou 001; Zuoqiang Shi (CoRR, 2015)

A heterogeneous stochastic FEM framework for elliptic PDEs. - Thomas Y. Hou 001; Pengfei Liu (J. Comput. Phys., 2015)

Sparse + low-energy decomposition for viscous conservation laws. - Thomas Y. Hou 001; Qin Li 007; Hayden Schaeffer (J. Comput. Phys., 2015)

On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. - Chunguang Liu; Zuoqiang Shi; Thomas Y. Hou 001 (Multiscale Model. Simul., 2015)

A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. - Zhiwen Zhang 001; Maolin Ci; Thomas Y. Hou 001 (Multiscale Model. Simul., 2015)

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods. - Eric T. Chung 001; Yalchin Efendiev; Thomas Y. Hou 001 (J. Comput. Phys., 2016)

An Accelerated Method for Nonlinear Elliptic PDE. - Hayden Schaeffer; Thomas Y. Hou 001 (J. Sci. Comput., 2016)

Sparse Time-Frequency Decomposition for Multiple Signals with Same Frequencies. - Thomas Y. Hou 001; Zuoqiang Shi (Adv. Data Sci. Adapt. Anal., 2017)

An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. - Thomas Y. Hou 001; Feng-Nan Hwang; Pengfei Liu; Chien-Chou Yao (J. Comput. Phys., 2017)

A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices. - Thomas Y. Hou 001; Qin Li 007; Pengchuan Zhang (Multiscale Model. Simul., 2017)

Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs. - Thomas Y. Hou 001; Qin Li 007; Pengchuan Zhang (Multiscale Model. Simul., 2017)

Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow. - Thomas Y. Hou 001; Tianling Jin; Pengfei Liu (J. Nonlinear Sci., 2018)

An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition. - Thomas Y. Hou 001; De Huang; Ka Chun Lam; Pengchuan Zhang (Multiscale Model. Simul., 2018)

A class of robust numerical methods for solving dynamical systems with multiple time scales. - Thomas Y. Hou 001; Zhongjian Wang; Zhiwen Zhang 001 (CoRR, 2019)

The subsampled Poincar ' e inequality for functional recovery. - Yifan Chen; Thomas Y. Hou 001 (CoRR, 2019)

A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition. - Thomas Y. Hou 001; De Huang; Ka Chun Lam; Ziyun Zhang (Multiscale Model. Simul., 2019)

A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach. - Thomas Y. Hou 001; Dingjiong Ma; Zhiwen Zhang 001 (Multiscale Model. Simul., 2019)

Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study. - Guo Luo; Thomas Y. Hou 001 (SIAM Rev., 2019)

Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data. - Yifan Chen; Thomas Y. Hou 001 (CoRR, 2020)

Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization. - Thomas Y. Hou 001; Zhenzhen Li; Ziyun Zhang (CoRR, 2020)

Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization. - Thomas Y. Hou 001; Zhenzhen Li; Ziyun Zhang (SIAM J. Math. Data Sci., 2020)

Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference. - Shumao Zhang; Pengchuan Zhang; Thomas Y. Hou 001 (ICML, 2021)

Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients. - Thomas Y. Hou 001; De Huang (CoRR, 2021)

Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations. - Yifan Chen; Thomas Y. Hou 001; Yixuan Wang (CoRR, 2021)

The nearly singular behavior of the 3D Navier-Stokes equations. - Thomas Y. Hou 001 (CoRR, 2021)

Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold. - Thomas Y. Hou 001; Zhenzhen Li; Ziyun Zhang (CoRR, 2021)

Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions. - Yifan Chen; Thomas Y. Hou 001; Yixuan Wang (Multiscale Model. Simul., 2021)

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 001; Anima Anandkumar (CoRR, 2022)

Exponentially Convergent Multiscale Finite Element Method. - Yifan Chen; Thomas Y. Hou 001; Yixuan Wang (CoRR, 2022)

Potential Singularity of the Axisymmetric Euler Equations with Cα Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case. - Thomas Y. Hou 001; Shumao Zhang (CoRR, 2022)

Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data. - Yifan Chen; Thomas Y. Hou 001 (Multiscale Model. Simul., 2022)

Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients. - Thomas Y. Hou 001; De Huang (Multiscale Model. Simul., 2023)

Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations. - Yifan Chen; Thomas Y. Hou 001; Yixuan Wang (Multiscale Model. Simul., 2023)

Potential Singularity of the 3D Euler Equations in the Interior Domain. - Thomas Y. Hou 001 (Found. Comput. Math., 2023)

Potentially Singular Behavior of the 3D Navier-Stokes Equations. - Thomas Y. Hou 001 (Found. Comput. Math., 2023)

Nearly self-similar blowup of generalized axisymmetric Navier-Stokes and Boussinesq equations. - Thomas Y. Hou 001 (CoRR, 2024)

Potential Singularity of the Axisymmetric Euler Equations with ( boldsymbol{C^{ alpha }} ) Initial Vorticity for a Large Range of ( boldsymbol{ alpha } ). - Thomas Y. Hou 001; Shumao Zhang (Multiscale Model. Simul., 2024)

KAN: Kolmogorov-Arnold Networks. - Ziming Liu; Yixuan Wang; Sachin Vaidya; Fabian Ruehle; James Halverson; Marin Soljacic; Thomas Y. Hou 001; Max Tegmark (ICLR, 2025)

On the expressiveness and spectral bias of KANs. - Yixuan Wang; Jonathan W. Siegel; Ziming Liu; Thomas Y. Hou 001 (ICLR, 2025)

Stable Nearly Self-Similar Blowup of the 2D Boussinesq and 3D Euler Equations with Smooth Data II: Rigorous Numerics. - Jiajie Chen; Thomas Y. Hou 001 (Multiscale Model. Simul., 2025)

High precision PINNs in unbounded domains: application to singularity formulation in PDEs. - Yixuan Wang; Ziming Liu; Zongyi Li; Anima Anandkumar; Thomas Y. Hou 001 (CoRR, 2025)