Welcome to my homepage

I am an Associate Professor at the Department of Mathematics, University of Wisconsin-Madison. I am also a faculty affiliate of the Institute for Foundations of Data Science (IFDS), a multi-University TRIPODS Phase II Initiative.

I received my PhD degree from the Courant Institute of Mathematical Sciences (CIMS) and the Center of Atmosphere and Ocean Science (CAOS), New York University (NYU) in May 2016. After that, I was a postdoc research associate at CIMS, NYU from June 2016 to May 2018. My PhD advisor and postdoc mentor were both Dr. Andrew Majda. My undergraduate major was Mechanical Engineering, Fudan University in Shanghai and I received my Master's degree at the School of Mathematical Sciences Fudan University, working with Dr. Jin Cheng, during which time I also visited the Department of Scientific Computing at Florida State University for one year, working with Dr. Max Gunzburger and Dr. Xiaoming Wang.

My research interests lie in contemporary applied mathematics: modeling complex systems, stochastic methods, numerical algorithms, geophysics, machine learning techniques, and general data science. Problems with large dimensional, turbulence, and partial information are mainly what I am concerned with. Mathematical and physical problems in uncertainty quantification (UQ), data assimilation, information theory, scientific machine learning, applied stochastic analysis, inverse problems, high-dimensional data analysis, and effective prediction all belong to my research topics. I am also devoted to proposing efficient and statistically accurate algorithms to alleviate the curse of dimensionality for large-dimensional complex dynamical systems with strong non-Gaussian features. In addition, I'm active in developing both dynamical and stochastic models and use these models to predict real-world phenomena related to atmosphere-ocean science, climate, and other complex systems such as the Madden-Julian Oscillation (MJO), the monsoon, the El Nino Southern Oscillation (ENSO) and the sea ice based on real observational data. My recent work also involves the development of new UQ and stochastic methods for material science. The mathematical and computational tools developed in my work can greatly interest diverse fields such as atmosphere-ocean science, climate, material science, neuroscience, excitable media, physics, and engineering.

I have teaching experience in different courses ranging from undergraduate to graduate levels, including Calculus, Numerical Methods, Uncertainty Quantification, Data Assimilation, Stochastic Computational Methods, Data-Driven Dynamical Systems. My lecture notes on the advanced course: "Topics in Applied Math: Uncertainty Quantification, Data Assimilation and Prediction" can be found through the "course" link above (or here). My outreach work for writing public articles, giving broader lectures for strengthening undergrad education and mentoring undergrads for summer research can be found here.

My new book "Stochastic Methods for Modeling and Predicting Complex Dynamical Systems --- Uncertainty Quantification, State Estimation, and Reduced-Order Models" published by Springer as part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS) has appeared. The link to the book on the Springer website is here. The book contains many sample codes, which can be used to learn the methods there!

I have a new paper "Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification — A Tutorial for Beginners" to appear at the Notices of the AMS. It is a short paper with many very simple examples to introduce UQ to beginners! Codes in Matlab and Python are available.

(Last updated 12/17/2024)