Search Results for author: Thomas Y. Hou

Found 6 papers, 1 papers with code

Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold

no code implementations20 Jul 2021 Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang

We show that on the manifold of fixed-rank and symmetric positive semi-definite matrices, the Riemannian gradient descent algorithm almost surely escapes some spurious critical points on the boundary of the manifold.

Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference

no code implementations12 May 2021 Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou

We propose a Multiscale Invertible Generative Network (MsIGN) and associated training algorithm that leverages multiscale structure to solve high-dimensional Bayesian inference.

Bayesian Inference Image Generation +1

Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients

no code implementations12 Feb 2021 Thomas Y. Hou, De Huang

In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equations with degenerate viscosity coefficients and smooth initial data of finite energy develop a potential finite-time locally self-similar singularity at the origin.

Analysis of PDEs Numerical Analysis Numerical Analysis Fluid Dynamics 35Q30, 35Q31, 35A21

A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition

no code implementations10 Apr 2018 Thomas Y. Hou, De Huang, Ka Chun Lam, Ziyun Zhang

In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework.

A sparse decomposition of low rank symmetric positive semi-definite matrices

1 code implementation3 Jul 2016 Thomas Y. Hou, Qin Li, Pengchuan Zhang

In this paper, we partition the indices from 1 to $N$ into several patches and propose to quantify the sparseness of a vector by the number of patches on which it is nonzero, which is called patch-wise sparseness.

Numerical Analysis

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