Shumao Zhang

collaborators

3 papers

math.AP2022

Potential Singularity of the Axisymmetric Euler Equations with $C^{α}$ Initial Vorticity for A Large Range of $α$ . Part II: the $N$ -Dimensional Case

Thomas Y. Hou, Shumao Zhang

In Part II of this sequence to our previous paper for the 3-dimensional Euler equations \cite{zhang2022potential}, we investigate potential singularity of the $n$ -diemnsional axisy…

math.AP2022

Potential Singularity of the Axisymmetric Euler Equations with $C^{α}$ Initial Vorticity for A Large Range of $α$

Thomas Y. Hou, Shumao Zhang

We provide numerical evidence for a potential finite-time self-similar singularity of the 3D axisymmetric Euler equations with no swirl and with $C^{α}$ initial vorticity for a large…

stat.ML2021

Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference

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. To…

Potential Singularity of the Axisymmetric Euler Equations with Cα Initial Vorticity for A Large Range of α. Part II: the N-Dimensional Case

Potential Singularity of the Axisymmetric Euler Equations with Cα Initial Vorticity for A Large Range of α

Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference

Potential Singularity of the Axisymmetric Euler Equations with $C^{α}$ Initial Vorticity for A Large Range of $α$ . Part II: the $N$ -Dimensional Case

Potential Singularity of the Axisymmetric Euler Equations with $C^{α}$ Initial Vorticity for A Large Range of $α$