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ORCIDThomas Y. Hou 0001
Thomas Yizhao Hou
Person information
- affiliation: Caltech, Computing & Mathematical Sciences Department, Pasadena, CA, USA
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2020 – today
- 2024
[i27]Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljacic, Thomas Y. Hou, Max Tegmark:
KAN: Kolmogorov-Arnold Networks. CoRR abs/2404.19756 (2024)- [i26]Thomas Y. Hou:
Nearly self-similar blowup of generalized axisymmetric Navier-Stokes and Boussinesq equations. CoRR abs/2405.10916 (2024) - 2023
- [j55]Thomas Y. Hou:
Potential Singularity of the 3D Euler Equations in the Interior Domain. Found. Comput. Math. 23(6): 2203-2249 (2023) - [j54]Thomas Y. Hou:
Potentially Singular Behavior of the 3D Navier-Stokes Equations. Found. Comput. Math. 23(6): 2251-2299 (2023) - [j53]Thomas Y. Hou, De Huang
:
Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients. Multiscale Model. Simul. 21(1): 218-268 (2023) - [j52]Yifan Chen, Thomas Y. Hou, Yixuan Wang:
Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations. Multiscale Model. Simul. 21(3): 849-883 (2023) - [i25]Jiajie Chen, Thomas Y. Hou:
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics. CoRR abs/2305.05660 (2023) - 2022
- [j51]Yifan Chen, Thomas Y. Hou:
Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data. Multiscale Model. Simul. 20(1): 188-219 (2022) - [i24]Haydn Maust, Zongyi Li, Yixuan Wang, Daniel V. Leibovici, Oscar P. Bruno, Thomas Y. Hou, Anima Anandkumar:
Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators. CoRR abs/2211.15960 (2022) - [i23]Yifan Chen, Thomas Y. Hou, Yixuan Wang:
Exponentially Convergent Multiscale Finite Element Method. CoRR abs/2212.00823 (2022) - [i22]Thomas Y. Hou, Shumao Zhang:
Potential Singularity of the Axisymmetric Euler Equations with Cα Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case. CoRR abs/2212.11912 (2022) - 2021
- [j50]Yifan Chen, Thomas Y. Hou, Yixuan Wang:
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions. Multiscale Model. Simul. 19(2): 980-1010 (2021) - [c1]Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou:
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference. ICML 2021: 12632-12641 - [i21]Thomas Y. Hou, De Huang:
Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients. CoRR abs/2102.06663 (2021) - [i20]Yifan Chen, Thomas Y. Hou, Yixuan Wang:
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations. CoRR abs/2105.04080 (2021) - [i19]Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou:
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference. CoRR abs/2105.05489 (2021) - [i18]Thomas Y. Hou:
Potential singularity of the 3D Euler equations in the interior domain. CoRR abs/2107.05870 (2021) - [i17]Thomas Y. Hou:
The nearly singular behavior of the 3D Navier-Stokes equations. CoRR abs/2107.06509 (2021) - [i16]Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang:
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold. CoRR abs/2107.09207 (2021) - 2020
- [j49]Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang:
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization. SIAM J. Math. Data Sci. 2(3): 840-871 (2020) - [i15]Yifan Chen, Thomas Y. Hou, Yixuan Wang:
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions. CoRR abs/2007.07418 (2020) - [i14]Yifan Chen, Thomas Y. Hou:
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data. CoRR abs/2010.04199 (2020) - [i13]Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang:
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization. CoRR abs/2012.15467 (2020)
2010 – 2019
- 2019
- [j48]Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang:
A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition. Multiscale Model. Simul. 17(1): 260-306 (2019) - [j47]Thomas Y. Hou, Dingjiong Ma, Zhiwen Zhang:
A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach. Multiscale Model. Simul. 17(2): 826-853 (2019) - [j46]Guo Luo, Thomas Y. Hou:
Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study. SIAM Rev. 61(4): 793-835 (2019) - [i12]Thomas Y. Hou, Zhongjian Wang, Zhiwen Zhang:
A class of robust numerical methods for solving dynamical systems with multiple time scales. CoRR abs/1909.04289 (2019) - [i11]Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang:
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization. CoRR abs/1911.12518 (2019) - [i10]Yifan Chen, Thomas Y. Hou:
The subsampled Poincar\' e inequality for functional recovery. CoRR abs/1912.08173 (2019) - 2018
- [j45]Thomas Y. Hou, Tianling Jin, Pengfei Liu:
Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow. J. Nonlinear Sci. 28(6): 2217-2247 (2018) - [j44]Thomas Y. Hou, De Huang, Ka Chun Lam, Pengchuan Zhang:
An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition. Multiscale Model. Simul. 16(2): 615-678 (2018) - [i9]Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang:
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition. CoRR abs/1804.03415 (2018) - 2017
- [j43]Thomas Y. Hou, Zuoqiang Shi:
Sparse Time-Frequency Decomposition for Multiple Signals with Same Frequencies. Adv. Data Sci. Adapt. Anal. 9(4): 1750010:1-1750010:17 (2017) - [j42]Thomas Y. Hou, Feng-Nan Hwang, Pengfei Liu, Chien-Chou Yao:
An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients. J. Comput. Phys. 336: 375-400 (2017) - [j41]Thomas Y. Hou, Qin Li, Pengchuan Zhang:
A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices. Multiscale Model. Simul. 15(1): 410-444 (2017) - [j40]Thomas Y. Hou, Qin Li, Pengchuan Zhang:
Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs. Multiscale Model. Simul. 15(2): 661-695 (2017) - 2016
- [j39]Eric T. Chung, Yalchin Efendiev, Thomas Y. Hou:
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods. J. Comput. Phys. 320: 69-95 (2016) - [j38]Hayden Schaeffer, Thomas Y. Hou:
An Accelerated Method for Nonlinear Elliptic PDE. J. Sci. Comput. 69(2): 556-580 (2016) - 2015
- [j37]Thomas Y. Hou, Pengfei Liu:
A heterogeneous stochastic FEM framework for elliptic PDEs. J. Comput. Phys. 281: 942-969 (2015) - [j36]Thomas Y. Hou, Qin Li, Hayden Schaeffer:
Sparse + low-energy decomposition for viscous conservation laws. J. Comput. Phys. 288: 150-166 (2015) - [j35]Zhiwen Zhang, Maolin Ci, Thomas Y. Hou:
A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. Multiscale Model. Simul. 13(1): 173-204 (2015) - [j34]Chunguang Liu, Zuoqiang Shi, Thomas Y. Hou:
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. Multiscale Model. Simul. 13(3): 790-811 (2015) - [i8]Thomas Y. Hou, Zuoqiang Shi:
Extracting a shape function for a signal with intra-wave frequency modulation. CoRR abs/1501.04704 (2015) - [i7]Chunguang Liu, Thomas Y. Hou, Zuoqiang Shi:
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data. CoRR abs/1501.04707 (2015) - [i6]Thomas Y. Hou, Zuoqiang Shi:
Sparse Time-Frequency decomposition for multiple signals with same frequencies. CoRR abs/1507.02037 (2015) - 2014
- [j33]Peyman Tavallali, Thomas Y. Hou, Zuoqiang Shi:
Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method. Multiscale Model. Simul. 12(4): 1458-1493 (2014) - [j32]Guo Luo, Thomas Y. Hou:
Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation. Multiscale Model. Simul. 12(4): 1722-1776 (2014) - 2013
- [j31]Thomas Y. Hou, X. Hu, Faiza Hussain:
Multiscale modeling of incompressible turbulent flows. J. Comput. Phys. 232(1): 383-396 (2013) - [j30]Mulin Cheng, Thomas Y. Hou, Zhiwen Zhang:
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations. J. Comput. Phys. 242: 753-776 (2013) - [j29]Mulin Cheng, Thomas Y. Hou, Zhiwen Zhang:
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms. J. Comput. Phys. 242: 843-868 (2013) - [j28]Yalchin Efendiev, Juan Galvis, Thomas Y. Hou:
Generalized multiscale finite element methods (GMsFEM). J. Comput. Phys. 251: 116-135 (2013) - [j27]Mulin Cheng, Thomas Y. Hou, Mike P. Yan, Zhiwen Zhang:
A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. SIAM/ASA J. Uncertain. Quantification 1(1): 452-493 (2013) - [i5]Yalchin Efendiev, Juan Galvis, Thomas Y. Hou:
Generalized Multiscale Finite Element Methods (GMsFEM). CoRR abs/1301.2866 (2013) - [i4]Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali:
Convergence of a data-driven time-frequency analysis method. CoRR abs/1303.7048 (2013) - [i3]Thomas Y. Hou, Zuoqiang Shi:
Sparse Time-Frequency decomposition by adaptive basis pursuit. CoRR abs/1311.1163 (2013) - [i2]Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali:
Sparse Time Frequency Representations and Dynamical Systems. CoRR abs/1312.0202 (2013) - 2011
- [j26]Thomas Y. Hou, Zuoqiang Shi:
Adaptive Data Analysis via Sparse Time-Frequency Representation. Adv. Data Sci. Adapt. Anal. 3(1-2): 1-28 (2011) - [j25]Thomas Y. Hou, Xue-Cheng Tai:
Introduction. Adv. Data Sci. Adapt. Anal. 3(1-2) (2011)
2000 – 2009
- 2009
- [j24]Thomas Y. Hou, Mike P. Yan, Zhaohua Wu:
A Variant of the EMD Method for Multi-Scale Data. Adv. Data Sci. Adapt. Anal. 1(4): 483-516 (2009) - 2008
- [j23]Thomas Y. Hou, Zuoqiang Shi:
An efficient semi-implicit immersed boundary method for the Navier-Stokes equations. J. Comput. Phys. 227(20): 8968-8991 (2008) - [j22]Thomas Y. Hou, Zuoqiang Shi:
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations. J. Comput. Phys. 227(21): 9138-9169 (2008) - [j21]Thomas Y. Hou, Danping Yang, Hongyu Ran:
Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier-Stokes Equations. Multiscale Model. Simul. 6(4): 1317-1346 (2008) - [i1]Thomas Y. Hou, Zuoqiang Shi:
Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations. CoRR abs/0801.2398 (2008) - 2007
- [j20]Thomas Y. Hou, Valentin G. Stredie, Theodore Yao-Tsu Wu:
Mathematical modeling and simulation of aquatic and aerial animal locomotion. J. Comput. Phys. 225(2): 1603-1631 (2007) - [j19]Thomas Y. Hou, Ruo Li:
Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226(1): 379-397 (2007) - 2006
- [j18]Shaoqiang Tang, Thomas Y. Hou, Wing Kam Liu:
A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations. J. Comput. Phys. 213(1): 57-85 (2006) - [j17]Thomas Y. Hou, Wuan Luo, Boris Rozovskii, Haomin Zhou:
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics. J. Comput. Phys. 216(2): 687-706 (2006) - [j16]Paul Dostert, Yalchin Efendiev, Thomas Y. Hou, Wuan Luo:
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification. J. Comput. Phys. 217(1): 123-142 (2006) - [j15]Yalchin Efendiev, Victor Ginting, Thomas Y. Hou, Richard E. Ewing:
Accurate multiscale finite element methods for two-phase flow simulations. J. Comput. Phys. 220(1): 155-174 (2006) - [j14]Thomas Y. Hou, Ruo Li:
Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations. J. Nonlinear Sci. 16(6): 639-664 (2006) - [j13]Thomas Y. Hou, Andrew Westhead, Danping Yang:
A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media. Multiscale Model. Simul. 5(4): 1087-1127 (2006) - [j12]Thomas Y. Hou, Congming Li:
On Global Well-Posedness of the Lagrangian Averaged Euler Equations. SIAM J. Math. Anal. 38(3): 782-794 (2006) - [j11]Yalchin Efendiev, Thomas Y. Hou, Wuan Luo:
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models. SIAM J. Sci. Comput. 28(2): 776-803 (2006) - 2005
- [j10]Mark S. Alber, Thomas Yizhao Hou, James A. Glazier, Yi Jiang:
Special Issue on Multiscale Modeling in Biology. Multiscale Model. Simul. 3(2) (2005) - [j9]Thomas Yizhao Hou, Petros Koumoutsakos:
Special Section on Multiscale Modeling in Materials and Life Sciences. Multiscale Model. Simul. 4(1): 213-214 (2005) - 2003
- [j8]Zhiming Chen, Thomas Y. Hou:
A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comput. 72(242): 541-576 (2003) - 2001
- [j7]Thomas Y. Hou, Pingwen Zhang:
A new stabilizing technique for boundary integral methods for water waves. Math. Comput. 70(235): 951-976 (2001) - 2000
- [j6]Yalchin R. Efendiev, Thomas Y. Hou, Xiao-hui Wu:
Convergence of a Nonconforming Multiscale Finite Element Method. SIAM J. Numer. Anal. 37(3): 888-910 (2000)
1990 – 1999
- 1999
- [j5]Thomas Y. Hou, Xiao-hui Wu, Zhiqiang Cai:
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. 68(227): 913-943 (1999) - [j4]Russel E. Caflisch, Thomas Y. Hou, John S. Lowengrub:
Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Math. Comput. 68(228): 1465-1496 (1999) - 1998
- [j3]Héctor D. Ceniceros, Thomas Y. Hou:
Convergence of a non-stiff boundary integral method for interfacial flows with surface tension. Math. Comput. 67(221): 137-182 (1998) - 1993
- [j2]Thomas Y. Hou, John S. Lowengrub, Michael J. Shelley:
The Convergence of an Exact Desingularization for Vortex Methods. SIAM J. Sci. Comput. 14(1): 1-18 (1993) - 1991
- [j1]Tony F. Chan, Thomas Y. Hou:
Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems. SIAM J. Sci. Comput. 12(6): 1471-1479 (1991)
Coauthor Index
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