Professor Tai's research fields mainly include numerical methods for partial differential equations (PDEs), inverse problems, optimization, computer vision, image processing and data science.
Professor Tai and his collaborators have made great contributions to computational mathematics, especially in the fields of numerical analysis and image processing. He is one of the inventors of AOS (additive operator splitting) algorithm, which has become a very popular algorithm in image processing using partial differential equations because of its efficiency and stability. He has also contributed several innovative algorithms in numerical analysis and research. His "obstacle problem algorithm" is "the first algorithm that has been proved to have the convergence speed of multigrid". He has also co-invented several new finite element methods for some singular perturbed PDEs which has been applied in practical engineering simulations.