Data Analysis and Assimilation, Bayesian Inference, Uncertainty Quantification
Multiscale and Stochastic Modeling, Analysis, and Simulation
Computational Fluid Dynamics, Combustion
Fast Time Integration
"The difficult is what takes a little time; the impossible is what takes a little longer." - Fridtjof Hansen, Nobel Peace Prize Laureate, 1922
(Winter 2017, Spring 2018) I am participating in Berkely Lab in School Settings, BLISS. As an ambassador for science education, I give lectures and demonstrations to K-6 students in the east bay elementary schools.
My CV is available for download here [link] (updated : Sep 11, 2017)
"The purpose of computing is insight, not numbers." - Richard Hamming
My research focuses on mathematical problems in prediction and uncertainty quantification of complex dynamical systems.
In particular I am intrested in robust and efficient computational methods to combine numerical prediction models with data,
which are scalable for big data and high-dimensional systems.
The mathematical framework of my research shares with research areas known as
Application areas of my research include but not limited to geophysical fluid systems and combustion models. You can find more details from my publications.
Work in progress
Importance sampling for computationally expensive target distributions
- In Bayesian inference or the calculation of statistical functionals, it is important to draw samples from posterior density.
Markov-Chain Monte-Carlo is one of the widely used methods, which draw samples throuhg Markov-Chain instead of independent samples.
However, MCMC suffers from burn-in time (a fraction of the first part of the chain is discarded for ergodicity of the chain) and a long chain length,
which are typical for high-dimensional systems.
Another method, importance sampling, draws samples from a proposal density that is easy to draw samples and closes to the posterior density.
Importance sampling uses independent samples and thus does not suffer from a long calculation time. However, unless the proposal density is similar to the posterior density,
particle collpase is inevitable in which most of the samples deliver no new information (in other words, the importance weights are marginal).
The MCMC based importance sampling method which I am working on is a fast (not suffering from long calculation time) and stable (no particle collapse) method mitigating disadvantages of MCMC and the standard importance sampling.
Effective particle filtering for non-Gaussian systems
- One important feasture of complex systems we encounter in science and engineering is non-Gaussianity.
Particle filtering is one of sequential importance sampling or data assimilation methods that can handle non-Gaussian systems but it is well-known that particle filter has limited applications for high-dimensional systems;
particle filtering suffers from poor performance such as particle collapse and degeneracy. One of my research work, the clustred particle filter published in PNAS, is a new class of stable particle filters through clustering and particle adjustment.
Now I am working on an improved version of the clustred particle filter applicable to dense observations in addition to sparse observations.
Bayesian parameter estimation for combustion
- At LBL, I am collborating with John Bell and Marcus Day to work on Bayesian parameter estimation of a hydrogen-oxygen combustion model, which is one of the research interests of DOE.
More specifically, we are interested in the estimation of chemial reaction rates for a hydrogen-oxygen combustion model using observations and prediction using massively parallel experiments. This research is supported by DOE. The parameter estimation of the combustion model has non-trivial characteristics that make it very challenging;
in addition to being non-Gaussian, the posterior density shows a wide range of scales and non-smooth compact support for the posterior density.
(with Y Kim, D Seung and H Cha) Science for high school students (in Korean), ETOOS, 2006, ISBN-13: 9788957352571
I find fun in teaching mathematics, physics and computer science, especially their interdisciplinary applications in science and engineering. Applyting theories to applications is one way to learn mathematics and science but I believe that it is more efficient to generalize ideas from examples (or experiences) and then apply to other applications. Thus motivating students from real-world examples is the primary goal of my teaching, which is followed by generalization of ideas and applications to other examples. Here are some comments from my students
Comments from my students
"You were so excited about the material and I liked that a lot! I enjoyed the part that you covered some basic stuff in the class when you realized that there are people from engineering and science, sitting there and they have absolutely no clue about what's going on! Thank you very much!"
"He did a great job of trying to incorporate real-world connections to help make what we were learning have value to us. He asked us questions to help us learn for ourselves and would take the time to show us alternative solutions or alternative problems so that we would be exposed to multiple ways of analyzing problems. Thank you for an enjoyable math experience from someone who hadn't been expecting one."
"He was amazing and gave helpful tips for not only this course but for future math and science courses."
"I hope you can find accomplishment in the fact that I have decided to double major in CS and Math because of what you have taught me."
"I really enjoyed the physics examples provided by Yoonsang. He created a very entertaining format to learn calculus."
"Extremely intelligent Yoonsang Lee gave lessons outside of math that pertained to many subjects. He related math to many applications, which at times complicated things."
"He will be a great professor one day because he is able to explain complex conceptual problems in simplistic terms!"
It is a good exercise to develop your own PDE solvers based on what you have learned in Numerical Analysis. However, for practical research computations, it is strongly recommended to use PDE solvers developed and refined by many researchers.
There are many PDE solvers freely available online. Among others, I recommend the following PDE solvers
- AMReX @ LBL and PETSc @ Argonne - for robust and efficient computations. Check out the following links.
Data assimilation combines a numerical forecast model with observational data to improve the prediction skill. If you are interested in testing/running data assimilation, please check the following programs.