Thomas Yizhao Hou

Charles Lee Powell Professor of Applied and Computational Mathematics

[*] Curriculum Vitae
[*] Recent Publications

[*] Back to the AMa home page.

Curriculum Vitae

University Address

Applied and Comput. Math., 9-94
California Institute of Technology
Pasadena, CA 91125
Tel: (626)-395-4546
Fax: (626)-578-0124
Email: hou@cms.caltech.edu

Education

B.S. (Mathematics), South China University of Technology, June 1982
M.S. (Mathematics), UCLA, March, 1985
Ph.D.(Mathematics), UCLA, 1987
Thesis Supervisor: Prof. Bjorn Engquist

Experience

Charles Lee Powell Professor of Applied and Computional Mathematics, Caltech, June 2004- present.

Professor of Applied and Computional Mathematics, Caltech, Feb 1998 - present.

Executive Officer of Applied and Computational Math, Caltech, July 2000 - June, 2006.

Associate Professor of Applied Mathematics, Caltech, June 1993 - Jan. 1998.

Associate Professor of Mathematics, Courant Institute, September 1992 - May1993.

Assstant Professor of Mathematics, Courant Institute, September 1989 - August 1992.

Visiting Member, Courant Institute, July 1987 - August 1989.

Invited Visiting Professor, Institute for Advanced Study, September 1991 - June 1992.

Research Interests


Homogenization, Multiscale Analysis and Computation;

Vortex Dynamics, Interface Problems, Multi-Phase Flows;

Singularity Formation of 3D Euler and Navier-Stokes Equations ;

Data Analysis.

Honors and Awards


Member of the National Academy of Sciences, 2024

The William Benter Prize in Applied Mathematics, 2024

The Householder Lecture, the Oak Ridge National Lab, 2024

The 2023 Birkhauser Distinguished Lecture, Journal of Mathematical Fluid Mechanics.

SIAM Ralph E. Kleinman Prize, 2023

SIAM Review SIGEST Award, 2019

Achievement Award, Southern California Chinese American Faculty Association, 2019

SIAM Outstanding Paper Prize, 2018

Fellow of the American Mathematical Society, 2012

Fellow of the American Academy of Arts and Sciences, 2011

Fellow of Society of Industrial and Applied Mathematics, 2009

Computational and Applied Sciences Award, the United States Association of Computational Mechanics, 2005

Morningside Gold Medal in Applied Mathematics, International Congress of Chinese Mathematicians, 2004

Invited Plenary Speaker, International Congress on Industrial and Applied Mathematicians, Sydney, 2003

James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, SIAM, 2001

Invited Speaker, International Congress of Mathematicians, Berlin, 1998

Francois N. Frenkiel Award for 1998, Division of Fluid Dynamics, American Physical Society.

Feng Kang Prize in Scientific Computing, 1997

Afred Sloan Fellow (1990-1992)

Richard C. DiPrima Outstanding Dissertation Prizes, Society of Industrial and Applied Mathematics, 2002 (Gang Hu) and 2006 (Xinwei Yu).

The Aisenstadt Chair, Center de Reserches Mathematiques, Universite de Montreal, 9/04-5/05.

The Aziz Lecturer, University of Maryland, 11/03.


Professional Service and Leadership


Member of SIAM Council, 2009 -- 2014

Director of Board of Governors, Institute of Mathematics and its Applications, January 2012 -- Dec. 2013.

Member of Board of Governors, Institute of Mathematics and its Applications, 2010 -- 2014.

Founding Editor-in-Chiefs


Founding Editor-in-Chief, SIAM Journal on Multiscale Modeling and Simulation, (Jan, 2002 -- Dec. 2007)

Founding Co-Editor-in-Chief, Advances in Adaptive Data Analysis, (Jan, 2009 -- Dec, 2015)

Co-Editor-in-Chief, Research in Mathematical Sciences, (Oct, 2014 -- Dec., 2023)

Editorial Boards

Editor Board, SIAM Journal on Multiscale Modeling and Simulation, (Jan, 2002-- present)

Editor Board, SIAM Journal on Numerical Analysis (June, 1992 -- Dec, 1997)

Editor, Mathematical Modelling and Numerical Analysis, (Oct, 1998 - Dec., 2001)

Editorial Board, Discrete and Continuous Dynamical Systems, Series B, (Aug, 2000 - July, 2006)

Editorial Board, Communications in Mathematical Sciences, (Jan, 2003 - Dec.2009)

Editorial Board, International Journal for Multiscale Computational Engineering, (April, 2004 - March, 2007)

Editorial Board, Applied Mathematics Letters, (Jan, 2012 - present)

Editorial Board, Journal of Computational Mathematics, (Jan, 2008 - present)


List of Publications

PUBLICATIONS



  1. Homogenization for Semilinear Hyperbolic Systems with Oscillatory Data, T. Y. Hou, Comm. Pure and Appl. Math. 41, 471-495 (1988).

  2. Particle Method Approximation of Oscillatory Solutions to Hyperbolic Differential Equations, B. Engquist and T. Y. Hou , SIAM J. Numer. Anal., 26, 289-319 (1989).

  3. The Convergence of the Point Vortex Method for the 2-D Euler Equations,  J. Goodman, T. Y. Hou and J. Lowengrub, Comm. Pure and Appl. Math., 43, 415-430(1990).

  4. Homogenization and Convergence of the Vortex Method for 2-D Euler Equations with Oscillatory Vorticity Fields, W. E and T. Y. Hou, Comm. Pure and Appl. Math., 43, 821-855 (1990)

  5. The Convergence of a Point Vortex Method for the 3-D Euler Equations, T. Y. Hou and J. Lowengrub, Comm. Pure and Appl. Math., 43 , 965-981(1990).

  6. Dispersive Approximations in Fluid Dynamics, T. Y. Hou and P. Lax, Comm. Pure and Appl. Math., 44, 1-40 (1991).

  7. Convergence of the Grid Free Point Vortex method for the 3-D Euler Equations, G.H. Cottet, J. Goodman and T. Y. Hou, SIAM J. Numer. Anal., 28, 291-307 (1991).

  8. Geometry Independent Convergence Results for Domain Decomposition Algorithms, T. F. Chan, T. Y. Hou and P. L. Lions SIAM J. Numer. Anal., 28, 378-391 (1991).

  9. Finite Difference Approximations for Partial Differential Equations with Rapidly Oscillating Coefficients, M. Avellaneda, T. Y. Hou and G. Papanicolaou, Mathematical Modelling and Numerical Analysis, 25, 693-710 (1991).

  10. Convergence of a Point Vortex Method for Vortex Sheets, ,  T. Y. Hou, J. Lowengrub and R. Krasny, SIAM J. Numer. Anal., 28 (2), 308-320 (1991).

  11. Homogenization of Linear Transport Equations with Oscillatory Vector Fields, T. Y. Hou and X. Xin, SIAM J. Appl. Math., 52, 34-45 (1992).

  12. Convergence of a Finite Difference Scheme for the Navier-Stokes Equations Using Vorticity Boundary Conditions, ,  T. Y. Hou and B. Wetton, SIAM J. Numer. Anal., 29, 615-639 (1992).

  13. Convergence of a Second Order Projection Method for the Navier-Stokes Equations with Boundaries, ,  T. Y. Hou and B. Wetton, SIAM J. Numer. Anal., 30, 609-629 (1993).

  14. Multi-Valued Solutions and Branch Point Singularities for Nonlinear Hyperbolic and Elliptic Systems, . Caflisch, N. Ercolani, T. Y. Hou, Y. Landis, Comm. Pure and Appl. Math., 46 , 453-499 (1993).

  15. Growth Rates for Linearized Motion of Fluid Interfaces Away from Equilibrium, J. T. Beale, T. Y. Hou and J. Lowengrub, Comm. Pure and Appl. Math. , 46 , 1269-1301 (1993).

  16. On the Stability of the Unsmoothed Fourier Method for Hyperbolic Equations, J. Goodman, T. Y. Hou and E. Tadmor, Numer. Math. , 67 , 93-129 (1994).

  17. Removing the Stiffness from Interfacial Flows with Surface Tension ,  T. Y. Hou, J. Lowengrub and M. Shelley, J. Comput Phys. , 114 , 312-338 (1994).

  18. Numerical Solutions to Free Boundary Problems, ,  T. Y. Hou, ACTA Numerica, , 4 , 335-415 (1995).

  19. Eulerian Capturing Methods Based on a Level Set Formulation for Incompressible Fluid Interfaces, ,  Y. C. Chang, T. Y. Hou, B. Merriman, and S. Osher, J. Comput Phys. , 124 , 449-464 (1996).

  20. Convergence of a Boundary Integral Method for Water Waves, J. T. Beale, T. Y. Hou and J. Lowengrub, SIAM J. Numer. Anal., . 33 , 1797-1843(1996).

  21. Well-Posedness of Linearized Motion for 3-D Water Waves Far From Equilibrium, T. Y. Hou, Z.-H. Teng, and P. Zhang, Comm in PDEs , 21 , 1551-1586 (1996).

  22. Converging Methods for the Computation of Propagating Solid-Solid Phase Boundaries, X. Zhong, T. Y. Hou, and P. LeFloch, J. Comput. Phys., 124 , 192-216 (1996).

  23. The Long-Time Motion of Vortex Sheets with Surface Tension ,  T. Y. Hou, J. Lowengrub and M. Shelley, Phys. of Fluid, A, 9 , 1933-1954 (1997).

  24. A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media ,  T. Y. Hou and X. H. Wu, J. Comput Phys. , 134 , 169-189, (1997).

  25. A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow, T. Y. Hou, Z. Li, S. Osher, and H. Zhao, J. Comput. Phys. , 134 , 236-252, (1997).

  26. Convergence of a Non-Stiff Boundary Integral Method for Interfacial Flows with Surface Tension ,  H. Ceniceros and T. Y. Hou, Math. Comput. , 67 , 137-182 (1998).

  27. Removing the Stiffness of Curvature in Computing 3-D Filaments ,  T. Y. Hou, I. Klapper and H. Si, J. Comput. Phys. , 143 , 628-664 (1998).

  28. Effect of Scaling Regime and Finite Scaling Range on the Relation between Power Laws in Physical and Spectral Domains, T. Y. Hou, X. H. Wu, S. Y. Chen and Y. Zhou, Phys. Review E. , 58 , 5841- (1998).

  29. Convergence of a Multiscale Finite Element Method for Elliptic Problems With Rapidly Oscillating Coefficients ,  T. Y. Hou, X. H. Wu, and Z.Q. Cai, Math. Comput. , 68 , 913-943, (1999).

  30. Dynamic Generation of Capillary Waves ,  H. Ceniceros and T. Y. Hou, Phys. Fluids, A , 11 (5) , 1042-1050 (1999).

  31. Numerical Study of Hele-Shaw Flow with Suction ,  H. Ceniceros, T. Y. Hou, and H. Si, Phys. Fluids, A , 11 (9) , 2471-2486, (1999).

  32. A Level-Set Approach to the Computation of Twinning and Phase Transition Dynamics, T. Y. Hou, P. Rosakis, and P. LeFloch, J. Comput. Phys. , 150 , 302-331 (1999).

  33. The Singular Perturbation of Surface Tension in Hele-Shaw Flow and The Effect of Noise ,  H. Ceniceros and T. Y. Hou, J. Fluid Mech. , 409 , 251-272 (2000).

  34. Convergence of A Nonconformal Multiscale Finite Element Method ,  Y. R. Efendiev, T. Y. Hou, and X. H. Wu, SIAM J. Numer. Anal. , 37 , 888-910 (2000)..

  35. A Mixed Multiscale Finite Element Method for Elliptic Problems with Oscillating Coefficients ,  Z. Chen and T. Y. Hou, Math. Comput., 72, No. 242 , 541-576, published electronically on June 28, 2002.

  36. An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions ,  H. Ceniceros and T. Y. Hou, J. Comput. Phys. , 172 , 1-31 2001.

  37. Boundary Integral Methods for Multi-Phase Problems in Fluid Dynamics and Materials Science ,  T. Y. Hou, J. Lowengrub, and M. Shelley, in J. Comput. Phys. , 169, No. 2 , 302-362 (2001).

  38. Convergence of A Boundary Integral Method for 3-D Water Waves ,  T. Y. Hou and P. Zhang, Discrete and Continuous Dynamical Systems, Series B , 2(1) , 1-34 (2002).

  39. Analysis of Upscaling Absolute Permeability ,  X. H. Wu, Y. Efendiev, and T. Y. Hou, Discrete and Continuous Dynamical Systems, Series B , 2(2), , 185-204(2002).

  40. Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios ,  J. Aarnes and T. Y. Hou, Acta Mathematicae Applicatae Sinica, , 18 No. 1 , 63-76 (2002).

  41. Singularity Formation in 3-D Vortex Sheets ,  T. Y. Hou, G. Hu, and P. Zhang, Phys of Fluids, , 15 No. 1 , 147-172 (2003).

  42. A Nearly Optimal Existence Result for Slightly Perturbed 3D Vortex Sheets ,  T. Y. Hou and G. Hu, Comm. in PDEs , 28, No.1/2, , 155-198 (2003).

  43. Numerical Approximations to Multiscale Solutions in Partial Differential Equations ,  T. Y. Hou, Frontier in Numerical Analysis , ed. J. F. Blowey, A. W. Craig, and T. Shardlow, Springer Publications, 241-302 (2003).

  44. Homogenization of Incompressible Euler Equation ,  T. Y. Hou, D. P. Yang, and K. Wang,

  45. Multiscale Modeling and Computation of Incompressible Flow ,  T. Y. Hou, Applied Mathematics Entering the 21st Century, Invited Talks from the ICIAM2003 Congress, ed. J. M. Hill and R. Moore, SIAM Publications, 177-210 (2004). J. Comput. Math. , 22, No.2, , 220-229 (2004).

  46. Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrove-Galerkin Formulation ,  T. Y. Hou, X. H. Wu and Y. Zhang Comm. Math. Sciences, , 2 No. 2 , 185-205 (2004).

  47. Geometric Properties and Non-blowup of 3-D Incompressible Euler Flow ,  J. Deng, T. Y. Hou, and X. Yu, Comm. in PDEs. , 30, No.1, , 225-243 (2005).

  48. Multiscale Numerical Methods for Singularly-Perturbed Convection Diffusion Equations ,  P. Park and T. Y. Hou, International Journal of Computational Methods , 1, No.1, , 17-65 (2004).

  49. Multiscale Finite Element Methods for Nonlinear Problems and Their Applications,  Y. Efendiev, T. Y. Hou, and V. Ginting, Comm. Math. Sci. , 2, No.4, , 553-589 (2004).

  50. A Modified Particle Method for Semilinear Hyperbolic Systems with Oscillatory Solutions ,  R. Fetecau and T. Y. Hou, Methods and Applications of Analysis , 11, No.4, , 573-604 (2004).

  51. Multiscale Analysis in Lagrangian Formulation for the 2-D Incompressible Euler Equation ,  T. Y. Hou, D. P. Yang, and H. Ran, Discrete and Continuous Dynamical Systems, Series A , 13(5) , 1153-1186, 2005.

  52. Global Well-Posedness of the Viscous Boussinesq Equations ,  T. Y. Hou and C. Li, Discrete and Continuous Dynamical Systems, Series A , 12(1), , 1-12, 2005.

  53. Improved Geometric Conditions for Non-blowup of the 3D Incompressible Euler Equation ,  J. Deng, T. Y. Hou, and X. Yu, Comm. in PDEs , 31, No. 2 , 293-306, 2006.

  54. Level Set Dynamics and Non-blowup of the 2D Quasi-Geostrophic Equation,  J. Deng, T. Y. Hou, R. Li, and X. Yu, Methods and Applications of Analysis , 13, No. 2 , 157-180, 2006.

  55. Wiener Chaos Expansions and Numerical Solutions of Randomly Forced Equations of Fluid Mechanics,  T. Y. Hou, W. Luo, B. Rozovskii, and H.M. Zhou, J. Comput. Phys. , 216 , 687-706 (2006).

  56. Coarse-gradient Langevin Algorithms for Dynamic Data Integration and Uncertainty Quantification,  P. Dostert, Y. Efendiev, T. Y. Hou, W. Luo, J. Comput. Phys. , 217 , 123-142 (2006).

  57. Parametric Vertical Coordinate Formulation for Multiscale, Boussinesq, and Non-Boussinesq Ocean Modeling ,  Y. T. Song and T. Y. Hou, Ocean Modeling , 11, , 298-332, 2006.

  58. A Pseudo-spectral Multiscale Method: Interfacial Conditions and Coarse Grid Equations ,  Shaoqiang Tang, T. Y. Hou, Wing Kam Liu, J. Comput. Phys. , 213 , 57-85, 2006.

  59. A Mathematical Framework of the Bridging Scale Method ,  Shaoqiang Tang, T. Y. Hou, Wing Kam Liu, Int. J. Numer. Meth. Engng., 65 , 1688-1713, 2006.

  60. Accurate Multiscale Finite Element Methods for Two-Phase Flow Simulations ,  Y. Efendiev, V. Ginting, T. Y. Hou, and R. Ewing, J. Comput. Phys., 220, , 155-174, 2006.

  61. On Global Well-Posedness of the Lagrangian Averaged Euler Equations ,  T. Y. Hou and C. Li, SIAM J. Math Anal., 38 (3) , 782-794, 2006.

  62. A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate ,  T. Y. Hou, V.G. Stredie, and T. Y. Wu, Comm. in Comput. Phys., 1 , 207-228, 2006.

  63. Mathematical Modeling and Simulation of Aquatic and Aerial Animal Locomotion ,  T. Y. Hou, V.G. Stredie, and T. Y. Wu, J. Comput. Phys. , 225 , 1603-1631, 2007.

  64. A Level Set Formulation for the 3D Incompressible Euler Equations ,  J. Deng, T. Y. Hou, and X. Yu, Methods and Applications of Analysis , 12 (4) , 427-440, 2005.

  65. Multiscale Computation of Isotropic Homogeneous Turbulent Flow ,  T. Y. Hou, D. P. Yang, and H. Ran, Contemporary Mathematics , 408 , 111-135, 2006. AMS Publ., Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory. ed. H. Ammari and H. Kang.

  66. Preconditioning of Markov Chain Monte Carlo Simulations Using Coarse-Scale Models ,  Y. Efendiev, T. Y. Hou and W. Luo, SIAM J. Sci. Comput. , 28(2) , 776-803, 2006.

  67. Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations ,  T. Y. Hou and R. Li, J. Nonlinear Science , 16(6) , 639-664, 2006.

  68. A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media ,  T. Y. Hou, A. Westhead, and D. P. Yang, SIAM Multiscale Modeling and Simulation , 5(4) , 1087-1127, 2006.

  69. Computing Nearly Singular Solutions Using Pseudo-Spectral Methods ,  T. Y. Hou and R. Li, J. Comput. Phys. , 226 , 379-397, 2007.

  70. Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations ,  T. Y. Hou and R. Li, Discrete and Continuous Dynamical Systems, Series A , 18(4) , 637-642, 2007.

  71. Multiscale Simulations of Porous Media Flows in Flow-Based Coordinate System ,  Y. Efendiev, T. Y. Hou, and T. Strinopoulos, Comput. Geoscience , 12 , 257-272, 2008, DOI 10.1007/s10596-007-9073-7.

  72. Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl ,  T. Y. Hou and C. Li, Commun. Pure Appl. Math. , 61(5) , 661--697, 2008. Published online Aug 27, 2007, DOI: 10.1002/cpa.20213.

  73. Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations ,  T. Y. Hou and R. Li, the Proceedings of 2006 Abel Symposium on Computational Mathematics , H. Munthe-Kaas and B. Owren (Eds.), Springer-Verlag, Berlin Heidelberg, 39--66, 2008.

  74. Multiscale Finite Element Methods for Porous Media Flows and Their Applications ,  Y. Efendiev and T. Y. Hou, Applied Numerical Mathematics , 57 , 577-596, 2007.

  75. Multiscale Analysis and Computation for the 3D Incompressible Navier-Stokes Equations ,  T. Y. Hou, D. P. Yang and H. Ran, SIAM Multiscale Modeling and Simulation , 6 (4) , 1317-1346, 2008, published online on March 26, 2008, DOI: 10.1137/070682046.

  76. Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data ,  T. Y. Hou, Z. Lei and C. Li, Commun PDEs, , 33 (9) , 1622-1637, 2008, DOI: 10.1080/03605300802108057.

  77. Blowup or No Blowup? The Interplay between Theory and Numerics ,  T. Y. Hou and R. Li, Physica D , 237 , 1937-1944, 2008, in the special issue of "Euler Equations: 250 Years On", published online Jan. 25, 2008, DOI:10.1016/j.physd.2008.01.018. .

  78. Flow Based Oversampling Technique for Multiscale Finite Element Methods ,  J. Chu, Y. Efendiev, V. Ginting, and T. Y. Hou, Advances in Water Resources , 31 , 599--608, 2008.

  79. Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations ,  T. Y. Hou and Z. Shi, J. Comput. Phys., , 227 , 9138-9169, 2008, DOI:10.1016/j.jcp.2008.03.002.

  80. An Efficient Semi-Implicit Immersed Boundary Method for the Navier-Stokes Equations ,  T. Y. Hou and Z. Shi, J. Comput. Phys., , 227 , 8968-8991, 2008, DOI:10.1016/j.jcp.2008.07.005.

  81. On the Stabilizing Effect of Convection in 3D Incompressible Flow ,  T. Y. Hou and Z. Lei, Commun. Pure Appl. Math. , 62(4) , 501--564, 2009. Published online June 10, 2008, DOI: 10.1002/cpa.20254.

  82. On the Partial Regularity of a 3D Model of the Navier-Stokes Equations ,  T. Y. Hou and Z. Lei, Commun. Math. Phys. , Commun. Math. Phys., 287(2) , 589--612, 2009. Published online on Nov. 20, 2008, DOI:10.1007/s00220-008-0689-9.

  83. Multiscale Analysis for Convection Dominated Transport Equations ,  T. Y. Hou and D. Liang, DCDS-A , 23 , 281-298, 2009, doi:10.3934/dcds.2009.23.281.

  84. Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations ,  T. Y. Hou, Acta Numerica , 18 , 277-346, 2009, doi: 10.1017/S0962492906420018.

  85. Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries ,  T. Y. Hou and B. Wetton, J. Comput. Math. , 27 (4) , 441-458, 2009.

  86. A Variant of the EMD Method for Multiscale Data, ,  T. Y. Hou, M. P. Yan, and Z. Wu, AADA , 1 (4) , 483-516, 2009.

  87. A New Multiscale Finite Element Method for High-Contrast Elliptic Interface Problems ,  C.-C. Chu, I. G. Graham, and T. Y. Hou, Math. Comput., 79 , 1915-1955, 2010.

  88. On Singularity Formation of a Nonlinear Nonlocal System ,  T. Y. Hou, C. Li, Z. Shi, S. Wang, and X. Yu, ARMA , 199 , 117-144, 2011.

  89. Adaptive Data Analysis via Sparse Time-Frequency Representation ,  T. Y. Hou and Z. Shi, Advances in Adaptive Data Analysis , 3 (1&2), 1-28, 2011. DOI: 10.1142/S1793536911000647.

  90. On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations ,  T. Y. Hou, Z. Shi, and S. Wang, Advances in Mathematics , 230, 607-641, 2012.

  91. Dynamic Growth Estimates of Maximum Vorticity for 3D Incompressible Euler Equations and the SQG Model ,  T. Y. Hou and Z. Shi, DCDS-A, 32 (5) , 1449-1463, 2012.

  92. Multiscale Modeling of Incompressible Turbulent Flows ,  T. Y. Hou, X. Hu, and F. Hussain, JCP , 232 , 383-396, 2013. DOI: 10.1016/j.jcp.2012.08.029.

  93. Data-Driven Time-Frequency Analysis ,  T. Y. Hou and Z. Shi, Applied and Comput. Harmon. Anal., Vol. 35(2), pp. 284-308, 2013, http://dx.doi.org/10.1016/j.acha.2012.10.001.

  94. A Decadal Microwave Record of Tropical Air Temperature from AMSU-A/Aqua Observations ,  Y. Shi, K. F. Li, Y. L. Yung, H. H. Aumann, Z. Shi, and T. Y. Hou, Climate Dynamics , 41 (5-6) , 1385-1405, 2013. DOI: 10.1007/s00382-013-1696-x.

  95. Numerical Simulation of Water Resources Problems: Models, Methods, and Trends ,  C. T. Miller, C. N. Dawsonb, M. W. Farthing, T. Y. Hou, J.F. Huange, C. E. Kees, C.T. Kelley, H. P. Langtangen, Advances in Water Resources , 51 , 405-437, 2013. DOI: 10.1016/j.advwatres.2012.05.008.

  96. A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equations I: Derivation and Algorithms ,  M. Cheng, T. Y. Hou, and Z. Zhang, JCP , 242 , 843-868, 2013. DOI:10.1016/j.jcp.2013.02.033.

  97. A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equations II: Adaptivity and Generalizations ,  M. Cheng, T. Y. Hou, and Z. Zhang, JCP , 242 , 753-776, 2013. DOI: 10.1016/j.jcp.2013.02.020.

  98. On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations, ,  T. Y. Hou, Z. Lei, G. Luo, S. Wang, and C. Zou, ARMA , , 2014. DOI: 10.1007/s00205-013-0717-6.

  99. Generalized Multiscale Finite Element Methods (GMsFEM) ,  Y. Efendiev, J. Galvis, and T. Y. Hou, JCP , 251 , 116-135, 2013. DOI: 10.1016/j.jcp.2013.04.045.

  100. A Multiscale Model Reduction Method for Partial Differential Equations, ,  M. Ci, T. Y. Hou and Z. Shi. M2AN , 48 , 449-474, 2014. DOI: 10.1051/m2an/2013115.

  101. Convergence of a Data-Driven Time-Frequency Analysis Method, ,  T. Y. Hou, Z. Shi, and P. Tavallali. Applied and Comput. Harmonic Analysis , 37 , 235-270, 2014. Doi: 10.1016/j.acha.2013.12.004 .

  102. A Data-driven Stochastic Method for Elliptic PDEs with Random Coefficients, ,  M. Cheng, T. Y. Hou, M. Yan, and Z. Zhang. SIAM/ASA J. Uncertainty Quantificatin , 1 , 452-493, 2013. DOI: 10.1137/130913249.

  103. Sparse Time Frequency Representation of Nonlinear and Nonstationary Data.,  T. Y. Hou and Z. Shi. Science China, Mathematics , 56 (No. 12) , 2489-2506, 2013. DOI: 10.1007/s11425-013-4733-7.

  104. Sparse Time Frequency Representation and Dynamical Systems. ,  T. Y. Hou, Z. Shi and P. Tavallali. Commun. Math. Sci., 13 (No. 3) 673-694, 2015.

  105. Potentially Singular Solutions of the 3D Incompressible Euler Equations, ,  G. Luo and T. Y. Hou. arXiv:1310.0497v2 [physics.flu-dyn], 2013.

  106. Potentially Singular Solutions of the 3D Axisymmetric Euler Equations,,  G. Luo and T. Y. Hou. PNAS , 111 no. 36 , 12968-12973, 2014. doi: 10.1073/pnas.1405238111, www.pnas.org/cgi/doi/10.1073/pnas.1405238111.

  107. Toward the Finite-Time Blowup of the 3D Incompressible Euler Equations: a Numerical Investigation,,  G. Luo and T. Y. Hou. SIAM MMS , 12 (No. 4) , 1722-176, 2014. DOI. 10.1137/140966411.

  108. On the Finite Time Blowup of a 1D Model for the 3D Incompressible Euler Equations. ,  T. Y. Hou and G. Luo. arXiv:1311.2613v1 [math.AP], 2013

  109. On the Finite Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations, ,  K. Choi, T. Y. Hou, A. Kiselev, G. G. Luo, V. Sverak, and Y. Yao. arXiv:1407.4776v2 [math.AP], CPAM, published online on May 3, 2017, DOI: 10.1002/cpa.21697.

  110. Self-Similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations, ,  T. Y. Hou and P. Liu. Research in Mathematical Sciences , 2:5 , 1-26, 2015. DOI 10.1186/s40687-015-0021-1.

  111. Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method. ,  P. Tavallali, T. Y. Hou, and Z. Shi. SIAM MMS , 12 (No. 4) , 1458-1493, 2014. DOI: 10.1137/140957767.

  112. A Heterogeneous Stochastic FEM Framework for Elliptic PDEs, ,  T. Y. Hou and P. Liu. JCP , 281 , 942-969, 2015. DOI: http://dx.doi.org/10.1016/j.jcp.2014.10.020.

  113. A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients, ,  Z. Zhang, M. Ci and T. Y. Hou. SIAM MMS , 13 (1) , 173-204, 2015. DOI. 10.1137/130948136.

  114. Sparse + Low-Energy Decomposition for Viscous Conservation Laws, ,  T. Y. Hou, Q. Li and H. Schaeffer. JCP , 288 , 150-166, 2015. DOI. http://dx.doi.org/10.1016/j.jcp.2015.02.019.

  115. On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data, ,  C. Liu, Z. Shi, and T. Y. Hou, SIAM MMS , 13 (3) , 790-811, 2015. DOI. 10.1137/141002098.

  116. Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods, ,  E. Chung, Y. Efendiev, and T. Y. Hou, JCP, 320 , 69-95, 2016. DOI: http://dx.doi.org/10.1016/j.jcp.2016.04.054.

  117. Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficients, ,  T. Y. Hou and P. Liu, DCDS-A, 36 (8) , 4451-4476, 2016. DOI:10.3934/dcds.2016.36.4451

  118. A Model Reduction Method for Elliptic PDEs with Random Input Using the Heterogeneous FEM Framework. ,  T. Y. Hou, P. Liu, and Z. Zhang, Bulletin of the Institute of Mathematics, 11 (1), 179-216, 2016.

  119. An Accelerated Method for Nonlinear Elliptic PDE. ,  H. Schaeffer and T. Y. Hou, J. Sci. Comput. , 69 , 556–580, 2016. DOI 10.1007/s10915-016-0215-8.

  120. Sparse Time-Frequency Decomposition by Dictionary Adaptation ,  T. Y. Hou and Z. Shi, Phil. Trans. R. Soc. A , 374 , 20150192, 2016. http://dx.doi.org/10.1098/rsta.2015.0192.

  121. Extracting a Shape Function for a Signal with Intra-Wave Frequency Modulation ,  T. Y. Hou and Z. Shi, Phil. Trans. R. Soc. A , 374, 20150194, 2016. http://dx.doi.org/10.1098/rsta.2015.0194.

  122. Identification of time-varying cable tension forces based on adaptive sparse time-frequency analysis of cable vibrations ,  Y. Bao, Z.Q. Shi, J. L. Beck, H. Li, T. Y. Hou, Structural Control and Health Monitoring, 24 (3), e1889, 2017, DOI: 10.1002/stc.1889

  123. A Sparse Decomposition of Low Rank Symmetric Positive Semi-definite Matrices, ,  T. Y. Hou, Q. Li, and P. Zhang, Multiscale Modeling and Simulation, 15 (1), 410-444, 2017. DOI: 10.1137/16M107760X.

  124. Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs, ,  T. Y. Hou, Q. Li, and P. Zhang, Multiscale Modeling and Simulation, 15 (2), 661-695, 2017. DOI: 10.1137/16M1077611 .

  125. An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients, ,  T. Y. Hou, F. N. Hwang, P. Liu, and C. C. Yao, JCP , 336, 375-400, 2017.

  126. Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow ,  T. Y. Hou, T. Jin, and P. Liu, JNLS , published online on March 1, 2017, DOI 10.1007/s00332-017-9370-9.

  127. Sparse Operator Compression of Higher-Order Elliptic Operators with Rough Coefficients ,  T. Y. Hou and P. Zhang, Research in Mathematical Sciences, 4:24, 2017, DOI 10.1186/s40687-017-0113-1

  128. A two-level method for sparse time-frequency representation of multiscale data ,  C. G. Liu, Z. Q. Shi, and T. Y. Hou, Science China Math , 60 (10), 1733-1752, 2017, doi: 10.1007/s11425-016-9.

  129. Sparse Time-Frequency decomposition for multiple signals with same frequencies ,  T. Y. Hou and Z. Q. Shi, Advances in Data Science and Adaptive Analysis , 9 (4), 1750010, 2017, DOI: 10.1142/S2424922X17500103.

  130. Global regularity for a family of 3D models of the axi-symmetric Navier-Stokes equations ,  T. Y. Hou, P. Liu, and F. Wang, Nonlinearity, 31 , 1940-1954, 2018, DOI. https://doi.org/10.1088/1361-6544/aaaa0b

  131. An adaptive fast solver for a general class of positive definite matrices via energy decomposition ,  T. Y. Hou, D. Huang, C. K. Lam, and P. Zhang, SIAM MMS, 16 (2), 615-678, 2018, DOI. 10.1137/17M1140686

  132. A Pseudo Knockoff Filter for Correlated Features ,  J. Chen, A. Hou and T. Y. Hou, Information and Inference: An IMA Journal, (20xx) 00, 1-29, 2018, doi: 10.1093/imaiai/iay012, published online on 7/17/2018.

  133. A Prototype Knockoff Filter for Group Selection with FDR Control ,  J. Chen, A. Hou and T. Y. Hou, Information and Inference: An IMA Journal, 2019, https://doi.org/10.1093/imaiai/iaz012, published online on July 11, 2019.

  134. A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition ,  T. Y. Hou, D. Huang, C. K. Lam, and Z. Zhang, SIAM MMS, 17 (1), 260-306, 2019, DOI. 10.1137/18M1180827

  135. A model reduction method for multiscale elliptic PDEs with random coefficiants using an optimization approach ,  T. Y. Hou, D. Ma, and Z. Zhang, SIAM MMS, 17 (2), 826-853, 2019, DOI. 10.1137/18M1205844.

  136. On the finite time blowup of the De Gregorio model for the 3D Euler equation ,  J. Chen, T. Y. Hou, and D. Huang, 2019, published online by CPAM on April 12, 2021, https://doi.org/10.1002/cpa.21991.

  137. Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^{1, alpha} Velocity and Boundary ,  J. Chen and T. Y. Hou, CMP, 383 (3), 1559-1667, 2021, DOI: https://doi.org/10.1007/s00220-021-04067-1, arXiv:1910.00173v2 [math.AP].

  138. Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: a Numerics Guided Study ,  G. Luo and T. Y. Hou, SIAM Review, 61 (4), 2019, DOI. 10.1137/19M1288061.

  139. Function Approximation via The Subsampled Poincare Inequality ,  Y. Chen and T. Y. Hou, DCDS-A, 41 (1), 169-199, 2021, doi: 10.3934/dcds.2020296.

  140. A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates ,  Z. Zhang, P. Rosakis, T. Y. Hou, and G. Ravichandran, J. R. Soc. Interface, 17: 20200175 , 2020, http://dx.doi.org/10.1098/rsif.2020.0175.

  141. Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization ,  T. Y. Hou, Z. Li, and Z. Zhang, SIMDS, 2(3) , 840-871, 2020, https://arxiv.org/abs/1911.12518.

  142. Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference ,  S. Zhang, P. Zhang and T. Y. Hou, Proceedings of the 38th International Conference on Machine Learning, PMLR, 139 , 12632--12641, 2021, http://proceedings.mlr.press/v139/zhang21z.html.

  143. Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization ,  T. Y. Hou, Z. Li, and Z. Zhang, https://arxiv.org/abs/2007.07418 [stat.ML], 2020.

  144. Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions ,  Y. Chen, T. Y. Hou, and Y. Wang, MMS, 19 (2), 980-1010, 2021, DOI: https://epubs.siam.org/doi/abs/10.1137/20M1352922, arXiv:2007.07418 [math.NA], 2020.

  145. Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations ,  Y. Chen, T. Y. Hou, and Y. Wang, MMS , 21 (3) , 849-883. arXiv:2105.04080 [math.NA], version 1 was posted on May 10, 2021.

  146. Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data ,  Y. Chen and T. Y. Hou, MMS, 20 (1), 188-219, 2022, DOI: https://doi.org/10.1137/20M1372214.

  147. Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients ,  T. Y. Hou and D. Huang, MMS, 21 (1), 218-268, 2023, DOI: 10.1137/22M1470906. http://arxiv.org/abs/2102.06663 [math.AP], 2021.

  148. Asymptotically Self-similar Blowup of the Hou-Luo Model for the 3D Euler Equations ,  J. Chen, T. Y. Hou and D. Huang, Annals of PDE, (2022) 8:24, https://doi.org/10.1007/s40818-022-00140-7. arXiv:2106.05422 [math.AP], 2021.

  149. Potential Singularity of the 3D Euler Equations in the Interior Domain ,  T. Y. Hou, JFoCM, 23 , 2203-2249, 2023, published online on September 7, 2022, DOI: https://doi.org/10.1007/s10208-022-09585-5. arXiv:2107.05870v2 [math.AP].

  150. Potentially Singular Behavior of the 3D Navier-Stokes Equations ,  T. Y. Hou, JFoCM, 23 , 2251-2299, 2023, published online on September 7, 2022, DOI: https://doi.org/10.1007/s10208-022-09578-4. arXiv:2107.06509v2 [physics.flu-dyn].

  151. A potential two-scale traveling wave singularity for 3D incompressible Euler equations ,  T. Y. Hou and D. Huang, Physica D, 435 , 133257, 2022, DOI: https://doi.org/10.1016/j.physd.2022.133257.

  152. On stability and instability of C^{1,alpha} singular solutions of the 3D Euler and 2D Boussinesq equations ,  J. Chen and T. Y. Hou, CMP, 405 , 405:112, 2024, DOI: ttps://doi.org/10.1007/s00220-024-04978-9, arXiv:2206.01296 [math.AP], 2022.

  153. Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold ,  T. Y. Hou, Z. Li, and Z. Zhang, arXiv:2107.09207 [math.OC], 2022.

  154. Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler enquations with smooth initial data I: Analysis ,  J. Chen and T. Y. Hou, arXiv:2210.07191 [math.AP], 2022.

  155. Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler enquations with smooth initial data II: Rigorous Numerics ,  J. Chen and T. Y. Hou, MMS, accepted. arXiv:2305.05660v2 [math.AP], 2023.

  156. Exponentially Convergent Multiscale Finite Element Method ,  Y. Chen, T. Y. Hou and Y. Wang, Comm Appl Math Comput, 2023, DOI: https://doi.org/10.1007/s42967-023-00260-2. arXiv:2212.00823 [math.NA], 2022.

  157. Potential singularity of the axisymmetric Euler equations with C^alpha initial vorticity for a large range of alpha. ,  T. Y. Hou and S. Zhang, MMS, 22 (4), 1326-1364, 2024, DOI. 10.1137/22M1542453. arXiv:2212.11912 [math.AP], 2022.

  158. Blowup Analysis for a quasi-exact 1D model of 3D Euler and Navier-Stokes ,  T. Y. Hou and Y. Wang, Nonlinearity, 37 , 035001, 2024, DOI: https://doi.org/10.1088/1361-6544/ad1c2f. arXiv:2306.04146[math.AP], 2023.

  159. KAN: Kolmogorov-Arnold Networks ,  Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. Soljacic, T. Y. Hou, and M. Tegmark, arXiv:2404.19756 [cs.LG], 2024.

  160. On the expressiveness and spectral bias of KANs ,  Y. Wang, J. Siegel, Z. Liu, and T. Y. Hou, arXiv:2410.01803v1 [cs.LG], 2024.

  161. L^2-based stability of blowup with log correction for semilinear heat equation ,  T. Y. Hou, V. T. Nguyen and Y. Wang, arXiv:2404.09410 [math.AP], 2024.

  162. Nearly self-similar blowup of generalized axisymmetric Navier-Stokes and Boussinesq equations ,  T. Y. Hou, arXiv:2405.10916 [math.AP], 2024.

  163. On stability of blowup solutions to the Complex Ginzburg-Landau equation in $R^d$ ,  J. Chen, T. Y. Hou, V. T. Nguyen and Y. Wang, arXiv:2407.15812 [math.AP], 2024.
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