In the past years, I have worked on

• Data Assimilation/Bayesian Inference
• Multiscale/Stochastic modeling, analysis, and simulation
• Geophysical Fluid Dynamics

Sea Ice Modeling and Data Assimilation MURI team website

Grants

• PI, An efficient numerical simulation method for sustainable material design, Albree Trust grant from Bank of America Private Bank, 2024, $10,000
• Co-PI, Integrated Foundations of Sensing, Modeling, and Data Assimilation for Sea Ice Prediction, June 1, 2020 - May 31, 2025, ONR MURI, $7,270,752,
• PI, Sub-linear complexity methods for multiscale problems without scale separation, August 1, 2019 - July 31, 2022, NSF DMS 1912999, $99,839.

Publications and preprints

Published

• K. Eikenberry, L. Liu, and Y. Lee, Post-Training Augmentation Invariance, Transactions on Machine Learning Research, accepted

• J. Han and Y. Lee, An analysis of the derivative-free loss method for solving PDEs, Research in Mathematical Sciences, accepted

• L. Liu, T. Li, A. Gelb, and Y. Lee, Entropy stable conservative flux form neural networks, SIAM Journal on Scientific Computing 107, 3 (2026)

• B. Choi and Y. Lee, Sampling error mitigation through spectrum smoothing: First experiments with ensemble transform Kalman filters and Lorenz models, Physica D, Vol 472, Feb 2025, 134436

• J. Han, Y. Lee, and A. Gelb, Learning In-between imagery dynamics via physical latent spaces, SIAM Journal on Scientific Computing, 46 (5), C608-C632, 2024.

• J. Han and Y. Lee, A stochastic approach for elliptic problems in perforated domains, Journal of Computational Physics, 519, 113426, 2024.

• T. Li, A. Gelb, and Y. Lee, A Structurally Informed Data Assimilation Approach for Nonlinear Partial Differential Equations, Journal of Computational Physics, 519, 113396, 2024.

• 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.

Preprints

• B. Choi, J. Han, and Yoonsang Lee, Weighted inhomogeneous regularization for inverse problems with indirect and incomplete measurement data, arXiv:2307.10448, 2024.

• 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.