<h1>Hou, Yizhao</h1>
<h2>Article from <a href="https://authors.library.caltech.edu">CaltechAUTHORS</a></h2>
<ul>
<li>Hou, Yizhao T. and Wang, Yixuan (2024) <a href="https://authors.library.caltech.edu/records/ca73j-gkv41">Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes</a>; Nonlinearity; Vol. 37; No. 3; 035001; <a href="https://doi.org/10.1088/1361-6544/ad1c2f">10.1088/1361-6544/ad1c2f</a></li>
<li>Chen, Yifan and Hou, Thomas Y., el al. (2023) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20230515-138520000.12">Exponentially Convergent Multiscale Finite Element Method</a>; Communications on Applied Mathematics and Computation; <a href="https://doi.org/10.1007/s42967-023-00260-2">10.1007/s42967-023-00260-2</a></li>
<li>Hou, Thomas Y. and Huang, De (2023) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20230530-441187700.9">Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients</a>; Multiscale Modeling and Simulation; Vol. 21; No. 1; 218-268; <a href="https://doi.org/10.1137/22m1470906">10.1137/22m1470906</a></li>
<li>Hou, Thomas Y. (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220919-258327700">Potentially Singular Behavior of the 3D Navier-Stokes Equations</a>; Foundations of Computational Mathematics; <a href="https://doi.org/10.1007/s10208-022-09578-4">10.1007/s10208-022-09578-4</a></li>
<li>Hou, Thomas Y. (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220919-922490500">Potential Singularity of the 3D Euler Equations in the Interior Domain</a>; Foundations of Computational Mathematics; <a href="https://doi.org/10.1007/s10208-022-09585-5">10.1007/s10208-022-09585-5</a></li>
<li>Hou, Thomas Y. and Huang, De (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220607-425321000">A potential two-scale traveling wave singularity for 3D incompressible Euler equations</a>; Physica D; Vol. 435; Art. No. 133257; <a href="https://doi.org/10.1016/j.physd.2022.133257">10.1016/j.physd.2022.133257</a></li>
<li>Chen, Jiajie and Hou, Thomas Y., el al. (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20221128-494241100.17">Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations</a>; Annals of PDE; Vol. 8; No. 2; Art. No. 24; <a href="https://doi.org/10.1007/s40818-022-00140-7">10.1007/s40818-022-00140-7</a></li>
<li>Chen, Yifan and Hou, Thomas Y. (2022) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220801-490095000">Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data</a>; Multiscale Modeling and Simulation; Vol. 20; No. 1; 188-219; <a href="https://doi.org/10.1137/20m1372214">10.1137/20m1372214</a></li>
<li>Zhang, Shumao and Zhang, Pengchuan, el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20220622-203755587">Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference</a>; Proceedings of Machine Learning Research; Vol. 139; 12632-12641; <a href="https://doi.org/10.48550/arXiv.2105.05489">10.48550/arXiv.2105.05489</a></li>
<li>Chen, Yifan and Hou, Thomas Y., el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20210922-170252834">Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions</a>; Multiscale Modeling and Simulation; Vol. 19; No. 2; 980-1010; <a href="https://doi.org/10.1137/20m1352922">10.1137/20m1352922</a></li>
<li>Chen, Jiajie and Hou, Thomas Y., el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200123-101534089">On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations</a>; Communications on Pure and Applied Mathematics; Vol. 74; No. 6; 1282-1350; <a href="https://doi.org/10.1002/cpa.21991">10.1002/cpa.21991</a></li>
<li>Chen, Jiajie and Hou, Thomas Y. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200122-142818756">Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^(1,α) Velocity and Boundary</a>; Communications in Mathematical Physics; Vol. 383; No. 3; 1559-1667; <a href="https://doi.org/10.1007/s00220-021-04067-1">10.1007/s00220-021-04067-1</a></li>
<li>Chen, Yifan and Hou, Thomas Y. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200122-075925100">Function approximation via the subsampled Poincaré inequality</a>; Discrete and Continuous Dynamical Systems - Series A; Vol. 41; No. 1; 169-199; <a href="https://doi.org/10.3934/dcds.2020296">10.3934/dcds.2020296</a></li>
<li>Chen, Jiajie and Hou, Anthony, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200124-145020991">A prototype knockoff filter for group selection with FDR control</a>; Information and Inference; Vol. 9; No. 2; 271-288; <a href="https://doi.org/10.1093/imaiai/iaz012">10.1093/imaiai/iaz012</a></li>
<li>Zhang, Zhiwen and Rosakis, Phoebus, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200123-103312153">A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates</a>; Journal of the Royal Society Interface; Vol. 17; No. 166; Art. No. 20200175; PMCID PMC7276546; <a href="https://doi.org/10.1098/rsif.2020.0175">10.1098/rsif.2020.0175</a></li>
<li>Luo, Guo and Hou, Thomas Y. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20191202-133631090">Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study</a>; SIAM Review; Vol. 61; No. 4; 793-835; <a href="https://doi.org/10.1137/19m1288061">10.1137/19m1288061</a></li>
<li>Hou, Thomas Y. and Lam, Ka Chun, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190620-093003600">Solving Bayesian inverse problems from the perspective of deep generative networks</a>; Computational Mechanics; Vol. 64; No. 2; 395-408; <a href="https://doi.org/10.1007/s00466-019-01739-7">10.1007/s00466-019-01739-7</a></li>
<li>Hou, Thomas Y. and Ma, Dingjiong, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190711-100817562">A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach</a>; Multiscale Modeling and Simulation; Vol. 17; No. 2; 826-853; <a href="https://doi.org/10.1137/18m1205844">10.1137/18m1205844</a></li>
<li>Chen, Jiajie and Hou, Anthony, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20191114-104110525">A pseudo knockoff filter for correlated features</a>; Information and Inference; Vol. 8; No. 2; 313-341; <a href="https://doi.org/10.1093/imaiai/iay012">10.1093/imaiai/iay012</a></li>
<li>Hou, Thomas Y. and Huang, De, el al. (2019) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190416-073721627">A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition</a>; Multiscale Modeling and Simulation; Vol. 17; No. 1; 260-306; <a href="https://doi.org/10.1137/18m1180827">10.1137/18m1180827</a></li>
<li>Hou, Thomas Y. and Jin, Tianling, el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170306-105506989">Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow</a>; Journal of Nonlinear Science; Vol. 28; No. 6; 2217-2247; <a href="https://doi.org/10.1007/s00332-017-9370-9">10.1007/s00332-017-9370-9</a></li>
<li>Hou, Thomas Y. and Liu, Pengfei, el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180405-130644881">Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations</a>; Nonlinearity; Vol. 31; No. 5; Art. No. 1940; <a href="https://doi.org/10.1088/1361-6544/aaaa0b">10.1088/1361-6544/aaaa0b</a></li>
<li>Hou, Thomas Y. and Huang, De, el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180718-150855095">An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition</a>; Multiscale Modeling and Simulation; Vol. 16; No. 2; 615-678; <a href="https://doi.org/10.1137/17M1140686">10.1137/17M1140686</a></li>
<li>Hou, Thomas Y. and Zhang, Pengchuan (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20171205-123956892">Sparse operator compression of higher-order elliptic operators with rough coefficients</a>; Research in the Mathematical Sciences; Vol. 4; No. 1; Art. No. 24; <a href="https://doi.org/10.1186/s40687-017-0113-1">10.1186/s40687-017-0113-1</a></li>
<li>Choi, Kyudong and Hou, Thomas Y., el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170509-075902405">On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations</a>; Communications on Pure and Applied Mathematics; Vol. 70; No. 11; 2218-2243; <a href="https://doi.org/10.1002/cpa.21697">10.1002/cpa.21697</a></li>
<li>Liu, ChunGuang and Shi, ZuoQiang, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170719-100127267">A two-level method for sparse time-frequency representation of multiscale data</a>; Science China Mathematics; Vol. 60; No. 10; 1733-1752; <a href="https://doi.org/10.1007/s11425-016-9088-9">10.1007/s11425-016-9088-9</a></li>
<li>Hou, Thomas Y. and Hwang, Feng-Nan, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170427-144329075">An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients</a>; Journal of Computational Physics; Vol. 336; 375-400; <a href="https://doi.org/10.1016/j.jcp.2017.02.002">10.1016/j.jcp.2017.02.002</a></li>
<li>Hou, Thomas Y. and Li, Qin, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170413-142311390">Exploring the locally low dimensional structure in solving random elliptic PDEs</a>; Multiscale Modeling &amp; Simulation; Vol. 15; No. 2; 661-695; <a href="https://doi.org/10.1137/16M1077611">10.1137/16M1077611</a></li>
<li>Hou, Thomas Y. and Li, Qin, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170413-141136299">A sparse decomposition of low rank symmetric positive semi-definite matrices</a>; Multiscale Modeling and Simulation; Vol. 15; No. 1; 410-444; <a href="https://doi.org/10.1137/16M107760X">10.1137/16M107760X</a></li>
<li>Bao, Yuequan and Shi, Zuoqiang, el al. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170214-074909079">Identification of time-varying cable tension forces based on adaptive sparse time-frequency analysis of cable vibrations</a>; Structural Control and Health Monitoring; Vol. 24; No. 3; Art. No. e1889; <a href="https://doi.org/10.1002/stc.1889">10.1002/stc.1889</a></li>
<li>Schaeffer, Hayden and Hou, Thomas Y. (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20161103-105632603">An Accelerated Method for Nonlinear Elliptic PDE</a>; Journal of Scientific Computing; Vol. 69; No. 2; 556-580; <a href="https://doi.org/10.1007/s10915-016-0215-8">10.1007/s10915-016-0215-8</a></li>
<li>Chung, Eric and Efendiev, Yalchin, el al. (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160624-151830832">Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods</a>; Journal of Computational Physics; Vol. 320; 69-95; <a href="https://doi.org/10.1016/j.jcp.2016.04.054">10.1016/j.jcp.2016.04.054</a></li>
<li>Hou, Thomas Y. and Liu, Pengfei (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160315-134934235">Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient</a>; Discrete and Continuous Dynamical Systems; Vol. 36; No. 8; 4451-4476; <a href="https://doi.org/10.3934/dcds.2016.36.4451">10.3934/dcds.2016.36.4451</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160315-095503958">Sparse time-frequency decomposition based on dictionary adaptation</a>; Philosophical Transactions A: Mathematical, Physical and Engineering Sciences; Vol. 374; No. 2065; Art. No. 20150192; PMCID PMC4792402; <a href="https://doi.org/10.1098/rsta.2015.0192">10.1098/rsta.2015.0192</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160315-095910709">Extracting a shape function for a signal with intra-wave frequency modulation</a>; Philosophical Transactions A: Mathematical, Physical and Engineering Sciences; Vol. 374; No. 2065; Art. No. 20150194; PMCID PMC4792404; <a href="https://doi.org/10.1098/rsta.2015.0194">10.1098/rsta.2015.0194</a></li>
<li>Huang, Norden E. and Daubechies, Ingrid, el al. (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160315-092552095">Adaptive data analysis: theory and applications</a>; Philosophical Transactions A: Mathematical, Physical and Engineering Sciences; Vol. 374; No. 2065; Art. No. 20150207; <a href="https://doi.org/10.1098/rsta.2015.0207">10.1098/rsta.2015.0207</a></li>
<li>Hou, Thomas Y. and Liu, Pengfei, el al. (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20161014-130127343">A Model Reduction Method for Elliptic PDEs with Random Input Using the Heterogeneous Stochastic FEM Framework</a>; Bulletin of the Intitute of Mathematics Academia Sinica; Vol. 11; No. 1; 179-216</li>
<li>Tavallali, Peyman and Hou, Thomas Y., el al. (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160404-090937429">On the convergence and accuracy of the cardiovascular intrinsic frequency method</a>; Royal Society Open Science; Vol. 2; No. 12; Art. No. 150475; PMCID PMC4807454; <a href="https://doi.org/10.1098/rsos.150475">10.1098/rsos.150475</a></li>
<li>Liu, Chunguang and Shi, Zuoqiang, el al. (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20151023-103928257">On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data</a>; Multiscale Modeling and Simulation; Vol. 13; No. 3; 790-811; <a href="https://doi.org/10.1137/141002098">10.1137/141002098</a></li>
<li>Zhang, Zhiwen and Ci, Maolin, el al. (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150501-105112539">A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients</a>; Multiscale Modeling and Simulation; Vol. 13; No. 1; 173-204; <a href="https://doi.org/10.1137/130948136">10.1137/130948136</a></li>
<li>Hou, Thomas Y. and Liu, Pengfei (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150115-154548810">A heterogeneous stochastic FEM framework for elliptic PDEs</a>; Journal of Computational Physics; Vol. 281; 942-969; <a href="https://doi.org/10.1016/j.jcp.2014.10.020">10.1016/j.jcp.2014.10.020</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang, el al. (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150519-083002339">Sparse Time Frequency Representations and Dynamical Systems</a>; Communications in Mathematical Sciences; Vol. 13; No. 3; 673-694; <a href="https://doi.org/10.4310/CMS.2015.v13.n3.a4">10.4310/CMS.2015.v13.n3.a4</a></li>
<li>Tavallali, Peyman and Hou, Thomas Y., el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150202-093859868">Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method</a>; Multiscale Modeling and Simulation; Vol. 12; No. 4; 1458-1493; <a href="https://doi.org/10.1137/140957767">10.1137/140957767</a></li>
<li>Luo, Guo and Hou, Thomas Y. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140825-230506377">Potentially singular solutions of the 3D axisymmetric Euler equations</a>; Proceedings of the National Academy of Sciences of the United States of America; Vol. 111; No. 36; 12968-12973; PMCID PMC4246962; <a href="https://doi.org/10.1073/pnas.1405238111">10.1073/pnas.1405238111</a></li>
<li>Pahlevan, Niema M. and Tavallali, Peyman, el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140825-134136758">Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications</a>; Journal of the Royal Society Interface; Vol. 11; No. 98; Art. No. 20140617; PMCID PMC4233710; <a href="https://doi.org/10.1098/rsif.2014.0617">10.1098/rsif.2014.0617</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang, el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140731-103641810">Convergence of a data-driven time–frequency analysis method</a>; Applied and Computational Harmonic Analysis; Vol. 37; No. 2; 235-270; <a href="https://doi.org/10.1016/j.acha.2013.12.004">10.1016/j.acha.2013.12.004</a></li>
<li>Zhang, Zhiwen and Hu, Xin, el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150112-104708436">Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient</a>; Communications in Computational Physics; Vol. 16; No. 3; 571-598; <a href="https://doi.org/10.4208/cicp.270913.020414a">10.4208/cicp.270913.020414a</a></li>
<li>Hou, Thomas Y. and Lei, Zhen, el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140422-134241808">On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations</a>; Archive for Rational Mechanics and Analysis; Vol. 212; No. 2; 683-706; <a href="https://doi.org/10.1007/s00205-013-0717-6">10.1007/s00205-013-0717-6</a></li>
<li>Luo, Guo and Hou, Thomas Y. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20150202-082208889">Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation</a>; Multiscale Modeling &amp; Simulation; Vol. 12; No. 4; 1722-1776; <a href="https://doi.org/10.1137/140966411">10.1137/140966411</a></li>
<li>Ci, Maolin and Hou, Thomas Y., el al. (2014) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140407-110251743">A Multiscale Model Reduction Method for Partial Differential Equations</a>; ESAIM-Mathematical Modelling and Numerical Analysis; Vol. 48; No. 2; 449-474; <a href="https://doi.org/10.1051/m2an/2013115">10.1051/m2an/2013115</a></li>
<li>Hou, Thomas Yizhao and Shi, Zuoqiang (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140113-074436396">Sparse time-frequency representation of nonlinear and nonstationary data</a>; Science China Mathematics; Vol. 56; No. 12; 2489-2506; <a href="https://doi.org/10.1007/s11425-013-4733-7">10.1007/s11425-013-4733-7</a></li>
<li>Efendiev, Yalchin and Galvis, Juan, el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20130830-131942975">Generalized multiscale finite element methods (GMsFEM)</a>; Journal of Computational Physics; Vol. 251; 116-135; <a href="https://doi.org/10.1016/j.jcp.2013.04.045">10.1016/j.jcp.2013.04.045</a></li>
<li>Shi, Yuan and Li, King-Fai, el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20140822-131136037">A decadal microwave record of tropical air temperature from AMSU-A/aqua observations</a>; Climate Dynamics; Vol. 41; No. 5-6; 1385-1405; <a href="https://doi.org/10.1007/s00382-013-1696-x">10.1007/s00382-013-1696-x</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20130725-100732399">Data-driven time–frequency analysis</a>; Applied and Computational Harmonic Analysis; Vol. 35; No. 2; 284-308; <a href="https://doi.org/10.1016/j.acha.2012.10.001">10.1016/j.acha.2012.10.001</a></li>
<li>Cheng, Mulin and Hou, Thomas Y., el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20130701-154101667">A dynamically bi-orthogonal method for time-dependent
stochastic partial differential equations II: Adaptivity and
generalizations</a>; Journal of Computational Physics; Vol. 242; 753-776; <a href="https://doi.org/10.1016/j.jcp.2013.02.020">10.1016/j.jcp.2013.02.020</a></li>
<li>Cheng, Mulin and Hou, Thomas Y., el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20130702-134527463">A dynamically bi-orthogonal method for time-dependent
stochastic partial differential equations I: Derivation and
algorithms</a>; Journal of Computational Physics; Vol. 242; 843-868; <a href="https://doi.org/10.1016/j.jcp.2013.02.033">10.1016/j.jcp.2013.02.033</a></li>
<li>Hou, T. Y. and Hu, X., el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20130104-102700776">Multiscale modeling of incompressible turbulent flows</a>; Journal of Computational Physics; Vol. 232; No. 1; 383-396; <a href="https://doi.org/10.1016/j.jcp.2012.08.029">10.1016/j.jcp.2012.08.029</a></li>
<li>Miller, Cass T. and Dawson, Clint N., el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20130305-095227632">Numerical simulation of water resources problems: Models, methods, and trends</a>; Advances in Water Resources; Vol. 51; 405-437; <a href="https://doi.org/10.1016/j.advwatres.2012.05.008">10.1016/j.advwatres.2012.05.008</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang, el al. (2012) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120523-112912673">On singularity formation of a 3D model for incompressible Navier–Stokes equations</a>; Advances in Mathematics; Vol. 230; No. 2; 607-641; <a href="https://doi.org/10.1016/j.aim.2012.02.015">10.1016/j.aim.2012.02.015</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang (2012) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120326-132813054">Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model</a>; Discrete and Continuous Dynamical Systems; Vol. 32; No. 5; 1449-1463; <a href="https://doi.org/10.3934/dcds.2012.32.1449">10.3934/dcds.2012.32.1449</a></li>
<li>Hou, Thomas Y. and Tai, Xue-Cheng (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180904-093329630">Introduction</a>; Advances in Adaptive Data Analysis; Vol. 3; No. 1-2; v-vi; <a href="https://doi.org/10.1142/S1793536911000672">10.1142/S1793536911000672</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120314-131024684">Adaptive data analysis via sparse time-frequency representation</a>; Advances in Adaptive Data Analysis; Vol. 3; No. 1-2; 1-28; <a href="https://doi.org/10.1142/S1793536911000647">10.1142/S1793536911000647</a></li>
<li>Hou, Thomas Y. and Li, Congming, el al. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110228-113453092">On Singularity Formation of a Nonlinear Nonlocal System</a>; Archive for Rational Mechanics and Analysis; Vol. 199; No. 1; 117-144; <a href="https://doi.org/10.1007/s00205-010-0319-5">10.1007/s00205-010-0319-5</a></li>
<li>Hou, Thomas Y. and Tai, Xue-Cheng (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20120322-080850518">Introduction</a>; Advances in Adaptive Data Analysis; Vol. 3; No. 1-2; v-vi; <a href="https://doi.org/10.1142/S1793536911000672">10.1142/S1793536911000672</a></li>
<li>Chu, C.-C. and Graham, I. G., el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20101012-100934632">A new multiscale finite element method for high-contrast elliptic interface problems</a>; Mathematics of Computation; Vol. 79; No. 272; 1915-1955</li>
<li>Hou, Thomas Y. and Lei, Zhen (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090528-090507806">On the stabilizing effect of convection in three-dimensional incompressible flows</a>; Communications on Pure and Applied Mathematics; Vol. 62; No. 4; 501-564; <a href="https://doi.org/10.1002/cpa.20254">10.1002/cpa.20254</a></li>
<li>Hou, Thomas Y. and Lei, Zhen (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090624-105309162">On the Partial Regularity of a 3D Model of the Navier-Stokes Equations</a>; Communications in Mathematical Physics; Vol. 287; No. 2; 589-612; <a href="https://doi.org/10.1007/s00220-008-0689-9">10.1007/s00220-008-0689-9</a></li>
<li>Hou, Thomas Y. and Liang, Dong (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUdcds09">Multiscale analysis for convection dominated transport equations</a>; Discrete and Continuous Dynamical Systems; Vol. 23; No. 1-2; 281-298; <a href="https://doi.org/10.3934/dcds.2009.23.281">10.3934/dcds.2009.23.281</a></li>
<li>Hou, Thomas Y. (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110321-155230291">Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations</a>; Acta Numerica; Vol. 18; 277-346; <a href="https://doi.org/10.1017/S0962492906420018">10.1017/S0962492906420018</a></li>
<li>Hou, Thomas Y. and Wetton, Brian R. (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20090819-164116745">Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries</a>; Journal of Computational Mathematics; Vol. 27; No. 4; 441-458; <a href="https://doi.org/10.4208/jcm.2009.27.4.012">10.4208/jcm.2009.27.4.012</a></li>
<li>Hou, Thomas Y. and Shi, Zuoqiang (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08b">Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations</a>; Journal of Computational Physics; Vol. 227; No. 21; 9138-9169; <a href="https://doi.org/10.1016/j.jcp.2008.03.002">10.1016/j.jcp.2008.03.002</a></li>
<li>Hou, T. Y. and Shi, Z. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUjcp08a">An efficient semi-implicit immersed boundary method
for the Navier–Stokes equations</a>; Journal of Computational Physics; Vol. 227; No. 20; 8968-8991; <a href="https://doi.org/10.1016/j.jcp.2008.07.005">10.1016/j.jcp.2008.07.005</a></li>
<li>Hou, Thomas Y. and Lei, Zhen, el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20091014-100827184">Global Regularity of the 3D Axi-symmetric
Navier-Stokes Equations with Anisotropic Data</a>; Communications in Partial Differential Equation; Vol. 33; No. 9; 1622-1637; <a href="https://doi.org/10.1080/03605300802108057">10.1080/03605300802108057</a></li>
<li>Efendiev, Y. and Hou, T., el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:EFEcg08">Multiscale simulations of porous media flows in flow-based coordinate system</a>; Computational Geosciences; Vol. 12; No. 3; 257-272; <a href="https://doi.org/10.1007/s10596-007-9073-7">10.1007/s10596-007-9073-7</a></li>
<li>Dostert, P. and Efendiev, Y., el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:DOScmame08">Multiscale finite element methods for stochastic porous media flow equations and application to uncertainty quantification</a>; Computer Methods in Applied Mechanics and Engineering; Vol. 197; No. 43-44; 3445-3455; <a href="https://doi.org/10.1016/j.cma.2008.02.030">10.1016/j.cma.2008.02.030</a></li>
<li>Hou, Thomas Y. and Li, Congming (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160322-093035560">Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl</a>; Communications on Pure and Applied Mathematics; Vol. 61; No. 5; 661-697; <a href="https://doi.org/10.1002/cpa.20212">10.1002/cpa.20212</a></li>
<li>Hou, Thomas Y. and Yang, Danping, el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUmms08">Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations</a>; Multiscale Modeling and Simulation; Vol. 6; No. 4; 1317-1346; <a href="https://doi.org/10.1137/070682046">10.1137/070682046</a></li>
<li>Hou, Thomas Y. and Li, Ruo (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160322-083351617">Computing nearly singular solutions using pseudo-spectral methods</a>; Journal of Computational Physics; Vol. 226; No. 1; 379-397; <a href="https://doi.org/10.1016/j.jcp.2007.04.014">10.1016/j.jcp.2007.04.014</a></li>
<li>Hou, T. Y. and Stredie, V. G., el al. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200310-145803950">Mathematical modeling and simulation of aquatic and aerial animal locomotion</a>; Journal of Computational Physics; Vol. 225; No. 2; 1603-1631; <a href="https://doi.org/10.1016/j.jcp.2007.02.015">10.1016/j.jcp.2007.02.015</a></li>
<li>Hou, Thomas Y. and Li, Ruo (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160322-091323469">Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations</a>; Discrete and Continuous Dynamical Systems; Vol. 18; No. 4; 637-642; <a href="https://doi.org/10.3934/dcds.2007.18.637">10.3934/dcds.2007.18.637</a></li>
<li>Efendiev, Y. and Hou, T. Y. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20100826-114814124">Multiscale finite element methods for porous media flows and their applications</a>; Applied Numerical Mathematics; Vol. 57; No. 5-7; 577-596; <a href="https://doi.org/10.1016/j.apnum.2006.07.009">10.1016/j.apnum.2006.07.009</a></li>
<li>Hou, Thomas Y. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUpnas07">Organized structures, memory, and the decay of turbulence</a>; Proceedings of the National Academy of Sciences of the United States of America; Vol. 104; No. 16; 6498-6499; PMCID PMC1871813; <a href="https://doi.org/10.1073/pnas.0700639104">10.1073/pnas.0700639104</a></li>
<li>Tang, Shao-Qiang and Liu, Wing K., el al. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:TANcpl07">Bridging Atomistic/Continuum Scales in Solids with Moving Dislocations</a>; Chinese Physics Letters; Vol. 24; No. 1; 161-164; <a href="https://doi.org/10.1088/0256-307X/24/1/044">10.1088/0256-307X/24/1/044</a></li>
<li>Hou, Thomas Y. and Westhead, Andrew, el al. (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUmms06">A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media</a>; Multiscale Modeling &amp; Simulation; Vol. 5; No. 4; 1087-1127; <a href="https://doi.org/10.1137/050646020">10.1137/050646020</a></li>
<li>Hou, Thomas Y. and Li, Ruo (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160322-090700507">Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations</a>; Journal of Nonlinear Science; Vol. 16; No. 6; 639-664; <a href="https://doi.org/10.1007/s00332-006-0800-3">10.1007/s00332-006-0800-3</a></li>
<li>Hou, Thomas Y. and Li, Congming (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjma06">On Global Well-Posedness of the Lagrangian Averaged Euler Equations</a>; SIAM Journal on Mathematical Analysis; Vol. 38; No. 3; 782-794; <a href="https://doi.org/10.1137/050625783">10.1137/050625783</a></li>
<li>Hou, T. Y. and Stredie, V. G., el al. (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUccp06">A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate</a>; Communications in Computational Physics; Vol. 1; No. 2; 207-228</li>
<li>Deng, Jian and Hou, Thomas Y., el al. (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409">Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation</a>; Communications in Partial Differential Equations; Vol. 31; No. 2; 293-306; <a href="https://doi.org/10.1080/03605300500358152">10.1080/03605300500358152</a></li>
<li>Efendiev, Y. and Hou, T., el al. (2006) <a href="https://resolver.caltech.edu/CaltechAUTHORS:EFEsiamjsc06">Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models</a>; SIAM Journal on Scientific Computing; Vol. 28; No. 2; 776-803; <a href="https://doi.org/10.1137/050628568">10.1137/050628568</a></li>
<li>Hou, Thomas Y. and Yang, Danping, el al. (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170408-161459048">Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation</a>; Discrete and Continuous Dynamical Systems; Vol. 13; No. 5; 1153-1186; <a href="https://doi.org/10.3934/dcds.2005.13.1153">10.3934/dcds.2005.13.1153</a></li>
<li>Hou, Thomas Y. (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20180404-083725024">Multiscale modelling and computation of fluid flow</a>; International Journal for Numerical Methods in Fluids; Vol. 47; No. 8-9; 707-719; <a href="https://doi.org/10.1002/fld.866">10.1002/fld.866</a></li>
<li>Deng, Jian and Hou, Thomas Y., el al. (2005) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20160322-075428588">Geometric Properties and Nonblowup of 3D Incompressible Euler Flow</a>; Communications in Partial Differential Equations; Vol. 30; No. 1-2; 225-243; <a href="https://doi.org/10.1081/PDE-200044488">10.1081/PDE-200044488</a></li>
<li>Fetecau, R. C. and Hou, T. Y. (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111013-071805594">A modified particle method for semilinear hyperbolic systems with oscillatory solutions</a>; Methods and Applications of Analysis; Vol. 11; No. 4; 573-604</li>
<li>Efendiev, Y. and Hou, T. Y., el al. (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111012-093928630">Multiscale Finite Element Methods for Nonlinear Problems and their Applications</a>; Communications in Mathematical Sciences; Vol. 2; No. 4; 553-589</li>
<li>Hou, Thomas Y. and Wu, Xiao-Hui, el al. (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20111014-070953819">Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation</a>; Communications in Mathematical Sciences; Vol. 2; No. 2; 185-205</li>
<li>Hou, Thomas Y. and Yang, Dan-ping, el al. (2004) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20110819-082640450">Homogenization of incompressible Euler equations</a>; Journal of Computational Mathematics; Vol. 22; No. 2; 220-229</li>
<li>Hou, Thomas Y. and Hu, Gang, el al. (2003) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUpof03">Singularity formation in three-dimensional vortex sheets</a>; Physics of Fluids; Vol. 15; No. 1; 147-172; <a href="https://doi.org/10.1063/1.1526100">10.1063/1.1526100</a></li>
<li>Chen, Zhiming and Hou, Thomas Y. (2002) <a href="https://resolver.caltech.edu/CaltechAUTHORS:CHEmc03">A mixed multiscale finite element method for elliptic problems with oscillating coefficients</a>; Mathematics of Computation; Vol. 72; No. 242; 541-576</li>
<li>Aarnes, Jørg and Hou, Thomas Y. (2002) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200221-160350446">Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios</a>; Acta Mathematicae Applicatae Sinica, English Series; Vol. 18; No. 1; 63-76; <a href="https://doi.org/10.1007/s102550200004">10.1007/s102550200004</a></li>
<li>Ceniceros, Hector D. and Hou, Thomas Y. (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:CENjfm00">The singular perturbation of surface tension in Hele-Shaw flows</a>; Journal of Fluid Mechanics; Vol. 409; 251-272; <a href="https://doi.org/10.1017/S0022112099007703">10.1017/S0022112099007703</a></li>
<li>Efendiev, Yalchin R. and Hou, Thomas Y., el al. (2000) <a href="https://resolver.caltech.edu/CaltechAUTHORS:EFEsiam00">Convergence of a nonconforming multiscale finite element method</a>; SIAM Journal on Numerical Analysis; Vol. 37; No. 3; 888-910; <a href="https://doi.org/10.1137/S0036142997330329">10.1137/S0036142997330329</a></li>
<li>Ceniceros, Hector D. and Hou, Thomas Y., el al. (1999) <a href="https://resolver.caltech.edu/CaltechAUTHORS:CENpof99">Numerical study of Hele-Shaw flow with suction</a>; Physics of Fluids; Vol. 11; No. 9; 2471-2486; <a href="https://doi.org/10.1063/1.870112">10.1063/1.870112</a></li>
<li>Ceniceros, Hector D. and Hou, Thomas Y. (1999) <a href="https://resolver.caltech.edu/CaltechAUTHORS:CENpof99a">Dynamic generation of capillary waves</a>; Physics of Fluids; Vol. 11; No. 5; 1042-1050; <a href="https://doi.org/10.1063/1.869975">10.1063/1.869975</a></li>
<li>Hou, Thomas Y. and Wu, Xiao-Hui, el al. (1998) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUpre98">Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces</a>; Physical Review E; Vol. 58; No. 5; 5841-5844; <a href="https://doi.org/10.1103/PhysRevE.58.5841">10.1103/PhysRevE.58.5841</a></li>
<li>Hou, Thomas Yizhao (1998) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUdmicm98">Numerical Study of Free Interface Problems Using Boundary Integral Methods</a>; Documenta Mathematica; Vol. Extra; No. Volume; 601-610</li>
<li>Hou, Thomas Y. and Wu, Xiao-Hui (1997) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170707-134035089">A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media</a>; Journal of Computational Physics; Vol. 134; No. 1; 169-189; <a href="https://doi.org/10.1006/jcph.1997.5682">10.1006/jcph.1997.5682</a></li>
<li>Beale, J. Thomas and Hou, Thomas Y., el al. (1996) <a href="https://resolver.caltech.edu/CaltechAUTHORS:BEAsiamjna96">Convergence of a Boundary Integral Method for Water Waves</a>; SIAM Journal on Numerical Analysis; Vol. 33; No. 5; 1797-1843; <a href="https://doi.org/10.1137/S0036142993245750">10.1137/S0036142993245750</a></li>
<li>Hou, Thomas Y. and Wetton, Brian T. R. (1993) <a href="https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjna93">Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries</a>; SIAM Journal on Numerical Analysis; Vol. 30; No. 3; 609-629; <a href="https://doi.org/10.1137/0730030">10.1137/0730030</a></li>
</ul>