Research Interest

My research interests lie in numerical analysis and scientific machine learning for partial differential equations. In particular, I am interested in 

• 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

• Towards better generalization: Weight Decay induces low-rank bias for neural networks, arXiv 2410.02176

• Let data talk: data-regularized operator learning theory for inverse problems, arXiv 2310.09854

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