Dartmouth College

27 N Main Street

Hanover, NH 03755

Office : 206 Kemeny Hall

email : yoonsang.lee at dartmouth.edu

I am an assistant professor in the Department of Mathematics at Dartmouth College. My research focuses 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.

- Computational Mathematics, Statistics and Physics
- Data Analysis and Assimilation, Bayesian Inference, Uncertainty Quantification
- Multiscale and Stochastic Modeling, Analysis, and Simulation
- Neural network-based methods for solving PDEs

- I am co-organizing a workshop at Banff, New Ideas in Computational Inverse Problems
- My work on sea ice numerics with Tongtong Li and Anne Gelb is featured at SIAM News
- I gave a talk at AMS East Sectional Meeting, Amherst, MA, Oct 1, 2022
- I presented the work with Jihun, a NN-based approach for homogenization, at SIAM Mathematics of Data Science. San Diego, CA, Sep 28, 2022.
- I was invited to talk at International Conference on Machine Learning and PDEs, Seoul, South Korea, Aug 28, 2022.
- I gave a seminar talk at Applied Mathematics seminar, Ewha Womans University, Jul 28, 2022.
- Tongtong Li presented our joint work at NAHOMCon 22, San Diego, CA, Jul 18, 2022
- Tongtong Li gave a talk about our joint work on sea ice numerics, SIAM Mathematics of Planet Earth, Pittsburgh, PA, July 2022.
- Matt Partno and I co-organized a minisymposium at SIAM MPE 2022, Pittsburgh, PA, July 2022.
- Jihun Han gave a talk about the joint work on "inhomogeneous regularization with limited and indirect data", SIAM Conference on Imaging Sciences. virtual, Mar 21, 2022.
- I gave a talk at Applied and Computational Mathematics seminar. UC Riverside, Feb 2, 2022.
- I presented at Machine Learning+X seminar. Brown University, Jan 7, 2022.

- (August 2018 - current) Assistant Professor, Department of Mathematics, Dartmouth College
- (June 2017 - July 2018) Postdoctoral Fellow, Center for Computational Sciences and Engineering @ Lawrence Berkeley Lab
- (June 2013 - May 2017) Postdoctoral Fellow, Courant Institute of Mathematical Sciences

- 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.

- G. Pease, Y. Lee, A. Gelb, and B. Keller, A Bayesian formulation for estimating the composition of Earth's crust, AGU Geophysical Research Letters, in revision.
- Z. Chen, A. Gelb, and Y. Lee, Designing Neural Networks for Hyperbolic Conservation Laws, arxiv:2211.14375
- T. Li, A. Gelb, and Y. Lee, Improving numerical accuracy for the viscous-plastic formulation of sea ice, arXiv:2206.10061, in revision.
- J. Han and Y. Lee, A Neural Network Approach for Homogenization of Multiscale Problems, SIAM Multiscale Modeling and Simulations, accepted.
- J. Han and Y. Lee, Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks, arXiv:2112.01254. Will appear in Springer Lecture Notes in Computational Sciences
- J. Han and Y. Lee, Inhomogenous Regularization in Inverse Problems, Journal of Computational and Applied Mathematics, Volume 428, 2023, 115193, ISSN 0377-0427
- Y Lee, l_p regularization for ensemble Kalman inversibion, SIAM J. Sci. Comput., 43(5), A3417--A3437, 2021.
- Y Lee, Fast time integration of parabolic equations with variable coefficients, submitted for publication [link]
- Y Lee, Parameter estimation in the stochastic superparameterization of two-layer quasigeostrophic flows, Research in the Mathematical Sciences 7, 14 (2020). https://doi.org/10.1007/s40687-020-00213-8 [link]
- Y Lee and B. Engquist Fast integrators for dynamical systems with several temporal scales, arXiv:1510.05728 [link]
- Y Lee, AJ Majda and D Qi, Stochastic superparameterization and multiscale filtering of turbulent tracers, SIAM Multiscale Modeling and Simulation, 15(1), 215-234, 2017 [link]
- Y Lee, 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]
- Y Lee and 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]
- Y Lee and B Engquist Multiscale numerical methods for advection-diffusion in incompressible turbulent flow fields, Journal of Computational Physics, 317(15), 33-46, 2016 [link]
- I Grooms and Y Lee, A framework for variational data assimilation with superparameterization, Nonlin. Processes. Geophys. 22(5), 601-611, 2015 [link]
- I Grooms, Y Lee 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]
- I Grooms, Y Lee 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]
- Y Lee and AJ Majda, Multiscale methods for data assimilation in turbulent systems, SIAM Multiscale Modeling and Simulation, 13(2), 691-713, 2015 [link]
- AJ Majda and Y Lee, Conceptual dynamical models for turbulence, Proceedings of the National Academy of Sciences, 111(18), 6548-6553, 2014 [link]
- I Grooms, Y Lee and AJ Majda, Ensemble Kalman filters for dynamical systems with unresolved turbulence, Journal of Computational Physics, 273(15), 435-452, 2014 [link]
- Y Lee and 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]
- G Ariel, B Engquist, S Kim, Y Lee, 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

- 2020 Winter - Math 126 Current Problems in Applied Mathematics
- 2019 Fall - Math 53 Partial Differential Equaitons
- 2019 Spring - Math 23 Differential Equations
- 2019 Winter - Math 106 Topics in Applied Mathematics I: Data-driven Uncertainty Quantification

I find fun in teaching mathematics, physics and computer science, especially their interdisciplinary applications in science and engineering. Applying 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.