Research Interest

My interest lies in data-driven physical problems, from the approach of applied math and also machine learning. Applied math provides us with well-explained modeling for complicated physical problems but its computability is limited by troubles like the curse of dimensionality, and numerical stability. Machine learning has the potential to bridge this gap, although the practical optimization stage could be quite a black box. I look forward to integrating these two fields elegantly so that we can still have a well-explained model as well as a scalable solver for the physical problem in interest.

Publications

Potential singularity of the axisymmetric Euler equations with $C^\alpha$ initial vorticity for a large range of $\alpha$. Part I: the $3$-dimensional case, Submitted, 2022

Thomas Y. Hou, Shumao Zhang (alphabetical order)
Potential singularity of the axisymmetric Euler equations with $C^\alpha$ initial vorticity for a large range of $\alpha$. Part II: the $N$-dimensional case, Submitted, 2022

Thomas Y. Hou, Shumao Zhang (alphabetical order)
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference, ICML, 2021

Shumao Zhang, Thomas Y. Hou, Pengchuan Zhang

Solving Bayesian Inverse Problems from the Perspective of Deep Generative Networks, Computational Mechanics, 2019

Thomas Y. Hou, Ka Chun Lam, Pengchuan Zhang, Shumao Zhang (alphabetical order)