I am a postdoctoral fellow at Center for Computational Sciences and Engineering at Lawrence Berkeley National Labratory, working on applied mathematics and computational issues in prediction and uncertainty quantification of complex dynamical systems. I am interested in particular in computational methods to efficiently combine numerical prediction models with data, which are scalable for big data and high-dimensional systems.

Before joining LBL, I was a postdoctoral fellow at Courant Institute, New York University woking with Professor Andrew J. Majda. I received my PhD in Mathematics under the supervision of Professor Bjorn Engquist at the University of Texas at Austin.

- Computational Mathematics, Statistics and Physics
- Data Analysis and Assimilation, Bayesian Inference, Uncertainty Quantification
- Multiscale and Stochastic Modeling, Analysis, and Simulation
- Computational Fluid Dynamics, Combustion
- Fast Time Integration

- (April 16-19, 2018) I will attend SIAM Conference on Uncertainty Quantification 2018 at Garden Grove CA and give a talk at the minisymposium "Nonlinear Filtering and Data Assimilation in Complex Dynamical Systems"
- (October 4, 2017) I gave a talk at UC Berkeley Applied Mathematics Seminar, 4-5pm in 891 Evans Hall. Check here for more details.
- (October 2, 2017) I gave a talk at UC Santa Cruz Applied Mathematics Colloquium, 4-5pm.
- (September 21, 2017) I gave a talk at TAMES 2017. The conference schdule can be found here [link].
- (July 20, 2017) I gave a talk at KSEA Berkeley chapter
- (July 11, 2017) I gave a talk at the mini-symposium "Data Assimilation and Nonlinear Filtering", SIAM Annual Meeting AN17, July 10-14, 2017. You can find more details here [link]
- (June 12, 2017) I moved to Center for Computational Sciences and Engineering @ LBNL
- (Arp 6, 2017) "Multiscale data assimilation and prediction using clustered particle filters", joint work with AJ Majda, is submitted for publication. In the paper, we propose and develop a new class of multiscale data assimilation method, the multiscale clustered paritcle filters, for Bayesian inference of high-dimensional complex dynamical systems. The paper studies the effect of observation model error on the estimation and prediction skill in the incorporation of reduced-order (i.e., low-dimensional approximation) prediction models.

- PhD in Mathematics, The University of Texas at Austin, USA, May 2013

Thesis title : Towards Seamless Multiscale Computations

Advisor : Bjorn Engquist - BS in Physics Education, College of Education, Seoul National University, South Korea
- BS in Mathematics, College of Natural Science, Seoul National University, South Korea

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

- data assimilation
- Bayesian inverse problems
- ensemble learning
- reduced-order modeling
- averaging and homogenization

Application areas of my research include but not limited to geophysical fluid systems and combustion models. You can find more details from my publications.

- 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 AJ Majda) Multiscale data assimilation and prediction using clustered particle filters, submitted for publication, 2017
- (with B Engquist) Fast integrators for dynamical systems with several temporal scales, arXiv:1510.05728 [link]
- (with AJ Majda and D Qi) Stochastic superparameterization and multiscale filtering of turbulent tracers, SIAM Multiscale Modeling and Simulation, 15(1), 215-234, 2017 [link]
- (widh AJ Majda and D Qi) Preventing catastrophic filter divergence using adaptive additive inflation for baroclinic turbulence, Monthly Weather Review, 145 (2), 669-682, DOI:http://dx.doi.org/10.1175/MWR-D-16-0121.1, 2017 [link]
- (with AJ Majda) State estimation and prediction using clustered particle filters, Proceedings of the National Academy of Sciences, 113 (51), 14609-14614, doi:10.1073/pnas.1617398113, 2016 [link]
- (with B Engquist) Multiscale numerical methods for advection-diffusion in incompressible turbulent flow fields, Journal of Computational Physics, 317(15), 33-46, 2016 [link]
- (with I Grooms) A framework for variational data assimilation with superparameterization, Nonlin. Processes. Geophys. 22(5), 601-611, 2015 [link]
- (with I Grooms and AJ Majda) Ensemble filtering and low-resolution model error: Additive inflation, stochastic parameterization, and model numerics, Monthly Weather Review, 143(10), 3912-3924, 2015 [link]
- (with I Grooms and AJ Majda) Numerical schemes for stochastic backscatter in the inverse cascade of quasigeostrophic turbulence, SIAM Multiscale Modeling and Simulaiton, 13(3), 1001-1021, 2015 [link]
- (with AJ Majda) Multiscale methods for data assimilation in turbulent systems, SIAM Multiscale Modeling and Simulation, 13(2), 691-713, 2015 [link]
- (with AJ Majda) Conceptual dynamical models for turbulence, Proceedings of the National Academy of Sciences, 111(18), 6548-6553, 2014 [link]
- (with I Grooms and AJ Majda) Ensemble Kalman filters for dynamical systems with unresolved turbulence, Journal of Computational Physics, 273(15), 435-452, 2014 [link]
- (with B. Engquist) Variable step size multiscale methods for stiff and highly oscillatory dynamical systems, Discrete and Continuous Dynamical Systems A, 34(3) 1079-1097, 2014 [link]
- (wtih G Ariel, B Engquist, S Kim and R Tsai) A multiscale method for highly oscillatory dynamical systems using a Poincare map type technique, Journal of Scientific Computing, 54(2-3), 247-268, 2013 [link]

- (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

- "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.