719 citations · 1.9k across the 57 of their papers we have counts for
58 papers
Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier-Stokes
Thomas Y. Hou, Yixuan Wang
We study the singularity formation of a quasi-exact 1D model proposed by Hou-Li in \cite{hou2008dynamic}. This model is based on an approximation of the axisymmetric Navier-Stokes…
Exponentially Convergent Multiscale Finite Element Method
Yifan Chen, Thomas Y. Hou, Yixuan Wang
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale s…
FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation
Adarsh Ganeshram, Haydn Maust, Valentin Duruisseaux +6
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs).…
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold
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 poi…
The potentially singular behavior of the 3D Navier-Stokes equations
Thomas Y. Hou
Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In t…
Potential singularity of the 3D Euler equations in the interior domain
Thomas Y. Hou
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this pape…