no code implementations • 20 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.
no code implementations • 12 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.
no code implementations • 12 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
no code implementations • 31 Dec 2020 • Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
The first one is a rank-1 matrix recovery problem.
no code implementations • 10 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.
1 code implementation • 3 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