Research
Research Interest
My research interests lie in numerical analysis and scientific machine learning for partial differential equations. In particular, I am interested inÂ
Scientific machine learning
Inverse problems
Randomized Sampling
My Google Scholar profile can be found here.
For Ph.D. applications: I am actively looking for Ph.D. Students who are interested in Scientific Machine Learning (SciML). The Ph.D. admission process is handled by the Department of Mathematical Sciences and you should apply here. You are encouraged to send your latest CV, an unofficial transcript, and our common research interests to my email.
Preprint
Peer Reviewed Journal Papers
Pseudo-differential integral autoencoder network for inverse PDE operators, Inverse Problems
Fast and high-order approximation of parabolic equations using hierarchical direct solvers and implicit Runge-Kutta methods, Communications on Applied Mathematics and Computation
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs, TMLR
Low-rank approximation for multiscale PDEs, Notices of the American Mathematical Society
Tensor-Structured Sketching for Constrained Least Squares, SIAM Journal on Matrix Analysis and Applications
A low-rank Schwarz method for radiative transfer equation with heterogeneous scattering coefficient, Multiscale Modeling & Simulation
Structured random sketching for PDE inverse problems, SIAM Journal on Matrix Analysis and Applications
Randomized sampling for basis function construction in generalized finite element methods, Multiscale Modeling & Simulation
Random sampling and efficient algorithms for multiscale PDEs, SIAM Journal on Scientific Computing
Online learning in optical tomography: a stochastic approach, Inverse Problems
Stability of stationary inverse transport equation in diffusion scaling, Inverse Problems
Stability of inverse transport equation in diffusion scaling and Fokker--Planck limit, SIAM Journal on Applied Mathematics
Peer Reviewed Conference Papers
Schwarz iteration method for elliptic equation with rough media based on random sampling, Proceedings of International Consortium of Chinese Mathematics 2019