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Efficient algorithms for numerical linear algebra, partial differential equations and integral equations. Application areas include physics, statistics, machine learning and deep learning.

Professor Cai's research aims to resolve grand computational challenges in scientific computing and data science by studying the mathematical properties and designing efficient algorithms.  Examples include modern matrix techniques for massive data analysis, adaptive solution for partial differential equations, etc. His recent interests involve studying mathematical structures in deep learning models for scalable computation and using deep learning approaches such as generative models for solving challenging scientific computing problems.

Professor Cai's work has appeared in Numerical Linear Algebra and Its Application, Numerische Mathematik, Journal of Computational Physics, SIAM Journal on Scientific Computing, SIAM Journal on Matrix Analysis and Applications, IEEE International Parallel and Distributed Processing Symposium, Conference on Uncertainty in Artificial Intelligence, and elsewhere.