83 results on '"Thomas Y. Hou"'
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2. On the expressiveness and spectral bias of KANs.
3. Nearly self-similar blowup of generalized axisymmetric Navier-Stokes and Boussinesq equations.
4. KAN: Kolmogorov-Arnold Networks.
5. Potentially Singular Behavior of the 3D Navier-Stokes Equations.
6. Potential Singularity of the 3D Euler Equations in the Interior Domain.
7. Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients.
8. Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations.
9. Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data.
10. Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics.
11. Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference.
12. Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions.
13. Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators.
14. Exponentially Convergent Multiscale Finite Element Method.
15. Potential Singularity of the Axisymmetric Euler Equations with Cα Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case.
16. Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization.
17. The nearly singular behavior of the 3D Navier-Stokes equations.
18. Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations.
19. Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold.
20. Potential singularity of the 3D Euler equations in the interior domain.
21. Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference.
22. Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients.
23. Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study.
24. A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition.
25. A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach.
26. An Adaptive Fast Solver for a General Class of Positive Definite Matrices Via Energy Decomposition.
27. Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow.
28. Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data.
29. Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization.
30. Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions.
31. An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients.
32. Sparse Time-Frequency Decomposition for Multiple Signals with Same Frequencies.
33. Exploring the Locally Low Dimensional Structure in Solving Random Elliptic PDEs.
34. A Sparse Decomposition of Low Rank Symmetric Positive Semidefinite Matrices.
35. A class of robust numerical methods for solving dynamical systems with multiple time scales.
36. The subsampled Poincar\' e inequality for functional recovery.
37. Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization.
38. Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods.
39. An Accelerated Method for Nonlinear Elliptic PDE.
40. A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition.
41. Sparse + low-energy decomposition for viscous conservation laws.
42. A heterogeneous stochastic FEM framework for elliptic PDEs.
43. On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data.
44. A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients.
45. Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method.
46. Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation.
47. Generalized multiscale finite element methods (GMsFEM).
48. A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations.
49. A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms.
50. Multiscale modeling of incompressible turbulent flows.
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