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Motivation: Main Research

As the observing technologies (sensors, cameras, camcorders, etc.) have matured over the years and the difficulties of data sharing have decreased, the amount of observation data has become immensely available (see this YouTube Video of swarm of starlings by National Geographic). My research is motivated by the need of making valid, useful and swift scientific discoveries from observation. For example, the story of how universal law of gravity was discovered traced back to Kepler's work on observation data of Mars' orbit.

To make a more precise statement of my research, the focus of my research is about designing and developing effective and efficient algorithms for making such discoveries. There are two major directions about my research:

In order to make accurate, convergent, and effective algorithms, I use theories and techniques from machine learning, numerical analysis, scientific computing, approximation theory, inverse problems, probability and statistics. Oftentimes, due to the gigantic size of the data set, the algorithms have to be scalable and efficient, hence I employ various techniques which reduce computing time: multi-scale representation, iterative solver, dimension reduction, domain decomposition, parallel computing, GPU computing (check out the Code section for details), etc. My research is interdisciplinary, it requries concrete knowledge of the observation technologies and underlying system, and it has applications in physics, biology, social science, and related engineering fields.

A complete list of publications can be found here.


In 2021:

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In 2012: