In the past years, I have worked on
Sea Ice Modeling and Data Assimilation MURI team website
B. Choi and Y. Lee, Sampling error mitigation through spectrum smoothing in ensemble data assimilation, arXiv:2404.00154, 2024.
T. Li, A. Gelb, and Y. Lee, A Structurally Informed Data Assimilation Approach for Nonlinear Partial Differential Equations, arXiv:2309.02585, 2024.
B. Choi, J. Han, and Yoonsang Lee, Weighted inhomogeneous regularization for inverse problems with indirect and incomplete measurement data, arXiv:2307.10448, 2024.
J. Han and Y. Lee, A stochastic approach for elliptic problems in perforated domains, arXiv:2403.11385, 2024, in revision, Journal of Computational Physics
J. Han, Y. Lee, and A. Gelb, Learning-between imagery dynamics via physical latent spaces,arXiv:2310.09495, 2023, in revision, SIAM Journal on Scientific Computing.
J. Han and Y. Lee, An analysis of the derivative-free loss method for solving PDEs, arXiv:2309.16829, 2023, submitted for publication in SIAM Journal on Numerical Analysis
Y. Lee, Sampling Error Correction in Ensemble Kalman Inversion, arXiv:2105.11341.
Y. Lee and B. Engquist, Fast integrators for dynamical systems with several temporal scales, arXiv:1510.05728.
Z. Chen, A. Gelb, and Y. Lee, Learning the dynamics for unknown hyperbolic conservation laws using deep neural networks, SIAM Journal on Scientific Computing, 46(2), A825–A850, 2024.
G. Pease, Y. Lee, A. Gelb, and B. Keller, A Bayesian formulation for estimating the composition of Earth’s crust, AGU Geophysical Research Letters: Solid Earth, 128 (7), July 2023.
T. Li, A. Gelb, and Y. Lee, Improving numerical accuracy for the viscous-plastic formulation of sea ice, Journal of Computational Physics, 487, August 2023, 112184.
J. Han and Y. Lee, Hierarchical learning to solve partial differential equations using physics-informed neural networks, Computational Science - ICCS 2023, Lecture Notes in Computer Science, Springer. 10475.548-562, 2023.
J. Han and Y. Lee, A neural network approach for homogenization of multiscale problems, SIAM Multiscale Modeling and Simulations, 21(2) 716–734, 2023.
J. Han and Y. Lee, Inhomogenous Regularization in Inverse Problems, Journal of Computational and Applied Mathematics, 428 115193, doi.org/10.1016/j.cam.2023.115193, 2023.
Y. Lee, lp-regularization for Ensemble Kalman Inversion, SIAM J. Sci. Comput., 43(5), A3417–A3437, 2021.
Y. Lee, Parameter estimation in the stochastic superparameterization of two-layer quasigeostrophic flows, Res Math Sci 7(14), 2020.
Y. Lee, A. J. Majda and D. Qi, Stochastic superparameterization and multiscale filtering of turbulent tracers, SIAM Multiscale Modeling and Simulation, 15(1), 215–234, 2017.
Y. Lee, A. J. Majda and D. Qi, Preventing catastrophic filter divergence using adaptive additive inflation for baroclinic turbulence, Monthly Weather Review, 145(2), 669-682, 2017.
Y. Lee and A. J. Majda, State estimation and prediction using clustered particle filters, Proceedings of the National Academy of Sciences of the United States of America, 113(51), 14609–14614, 2016.
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.
I. Grooms and Y. Lee, A framework for variational data assimilation with superparameterization, Nonlin. Processes. Geophys. 22, 601–611, 2015.
I. Grooms, Y. Lee and A. J. Majda, Ensemble filtering and low-resolution model error: Covariance inflation, stochastic parameterization, and model numerics, Mon. Wea. Rev. 143, 3912–3924, 2015.
I. Grooms, Y. Lee and A. J. Majda, Numerical schemes for stochastic backscatter in the inverse cascade of quasigeostrophic turbulence, SIAM Multiscale Modeling and Simulation, 13(3), 1001–1021, 2015.
Y. Lee and A. J. Majda, Multiscale methods for data assimilation in turbulent systems, SIAM Multiscale Modeling and Simulation, 13(2), 691–173, 2015.
A. J. Majda and Y. Lee, Conceptual dynamical models for turbulence, Proceedings of the National Academy of Sciences of the United States of America, 111 18, 6548–6553, 2014.
I. Grooms, Y. Lee and A. J. Majda, Ensemble Kalman filters for dynamical systems with unresolved turbulence, Journal of Computational Physics, 273 15, 435–452, 2014.
Y. Lee and B. Engquist Variable step size multiscale methods for stiff and highly oscillatory dynamical systems, Discrete and Continuous Dynamical Systems - Series A, 34 3, 1079–1097, 2014.
G. Ariel, B. Engquist, S. Kim, Y. Lee and R. Tsai, A multiscale method for highly oscillatory dynamical systems using a Poincarè map type technique, Journal of Scientific Computing, 54 2-3, 247–268, 2013.