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 am also the Secretary of the SIAM MPE and a member of a US CLIVAR Working Group.I am an editor of Physica D: Nonlinear Phenomena (Elsevier) and Nonlinear Processes in Geophysics (EGU).

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.

Research summary (Please see my research and publications pages for more details).

My research interests lie in contemporary applied mathematics: modeling complex systems, stochastic methods, machine learning techniques and applications, digital twins, causal inference, numerical algorithms, geophysics, and general data science. Problems with large dimensions, 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 are among 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, and other complex systems such as the Madden-Julian Oscillation (MJO), the monsoon, the El Niño 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 have a significant impact on diverse fields, including atmospheric-ocean science, materials science, neuroscience, excitable media, physics, and engineering.

Some of my research are highlighted by media: SIAM News, SIAM DSWeb, EoS, Springer Nature Research Communities, Miragenews, The National, etc.

Educational materials.

Over the years, I have noticed a recurring challenge in teaching applied mathematics: many powerful ideas are first introduced through examples that are already too complicated for initial understanding. While finishing our book Applied Mathematics Toolkit: Modeling • Data • Algorithms, Charlotte Moser and I decided to explore a different approach in parallel by creating a short video series built around a simple principle: one concept • one example. Each video is 5–10 minutes long, focuses on a single idea, and uses deliberately simple examples to support first exposure, intuition building, and efficient review. So far, we have completed two modules (Statistical Toolkit and Machine Learning Toolkit), with three more in progress (Applied Analysis Toolkit, Dynamical Systems Toolkit, and Stochastic Toolkit). The series is intended primarily for upper-level undergraduates, early graduate students, and researchers seeking a clean conceptual entry point before engaging with more technical treatments. The videos are presented by Charlotte Moser, an applied mathematician with extensive experience presenting research at international conferences, and are shared openly in the hope that they may be useful for learning, teaching, or quick conceptual review. The full collection is available on her YouTube channel and RedNote. We hope this format offers a small but meaningful contribution toward making applied mathematics more accessible, modular, and reusable across disciplines. If you would like to follow the release of future modules, you are welcome to subscribe. We also warmly welcome feedback, suggestions for future topics, or ideas for collaboration.

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

Openings:

I am looking for one highly motivated high-school student from Madison or the nearby area in Dane County to participate in a 2026 summer research program at UW-Madison, supported by the Army Educational Outreach Program (AEOP). The research topic will be causal inference and model identification from ocean data. If you are interested, please send me your CV and a short self-description.

I am always looking for highly motivated PhD students to work with me. If you have been admitted to our Math PhD program and are interested in my work (even if you start as a pure math student), please feel free to contact me.

(Last updated 02/08/2026)