Thomas Y. Hou

1. KAN: Kolmogorov-Arnold Networks
   2024/04/30 by Ziming Liu, Yixuan Wang, Liu, Ziming +13 · 16 voices · 177 citations
   Computer Science · #Cognitive Computing and Networks #Computability, Logic, AI Algorithms #cond-mat.dis-nn #cs.AI #cs.LG #stat.ML
2. Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics
   2023/05/09 by Jiajie Chen, Chen, Jiajie, Thomas Y. Hou +1 · 8 citations
   Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
3. Why nonconservative schemes converge to wrong solutions: error analysis
   1994/01/01 by Thomas Y. Hou, Philippe G. LeFloch · 2 citations
   Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems
4. Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations
   2021/06/09 by Jiajie Chen, Thomas Y. Hou, Chen, Jiajie +3 · 1 voice · 1 citation
   #math.AP
5. Potential singularity of the 3D Euler equations in the interior domain
   2021/07/13 by Thomas Y. Hou, Hou, Thomas Y. · 1 citation
   Mathematics · Engineering · #Navier-Stokes equation solutions #Computational Fluid Dynamics and Aerodynamics #Advanced Mathematical Physics Problems
6. Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part II: the N-Dimensional Case
   2022/12/22 by Thomas Y. Hou, Shumao Zhang, Hou, Thomas Y. +1 · 1 citation
   Mathematics · Engineering · #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows #Computational Fluid Dynamics and Aerodynamics
7. Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α
   2022/12/22 by Thomas Y. Hou, Shumao Zhang, Hou, Thomas Y. +1 · 1 citation
   Engineering · Mathematics · #35Q31 #65M06 #65M20 #65M60 #76B03 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
8. Geometric properties and non-blowup of 3-D incompressible Euler flow
   2004/02/12 by Jian Deng, Thomas Y. Hou, Deng, Jian +3 · 1 citation
   Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows #Tribology and Lubrication Engineering #math-ph #math.MP #msc:76B03
9. Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier-Stokes
   2023/06/07 by Thomas Y. Hou, Hou, Thomas Y., Yixuan Wang +1 · 1 citation
   Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
10. Exponentially convergent multiscale methods for high frequency\n heterogeneous Helmholtz equations
    2021/05/09 by Yifan Chen, Thomas Y. Hou, Chen, Yifan +3 · 1 citation
    Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Advanced Numerical Methods in Computational Mathematics
11. Nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations
    2024/05/17 by Thomas Y. Hou, Hou, Thomas Y. · 1 citation
    Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
12. High precision PINNs in unbounded domains: application to singularity formulation in PDEs
    2025/06/24 by Yixuan Wang, Ziming Liu, Wang, Yixuan +7 · 3 citations
    Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering
13. Analytic finite-rank corrections for singularly weighted estimates in a computer-assisted proof of 3D Euler singularity
    2026/07/16 by Jiajie Chen, Thomas Y. Hou
    #math.AP #cs.NA #math.NA