Publications

You can also find my articles on my Google Scholar profile.

Structure-preserving dynamics modeling

• Structure preserving reversible and irreversible bracket dynamics for deep graph neural networks [Preprint]
  A Gruber, K Lee, N Trask
  Advances in Neural Information Processing Systems (NeurIPS), 2023

• Structure-preserving sparse identification of nonlinear dynamics for data-driven modeling [Paper][Code]
  K Lee, N Trask, P Stinis
  Mathematical and Scientific Machine Learning (MSML), 2022

• Machine learning structure preserving brackets for forecasting irreversible processes [Paper]
  K Lee, N Trask, and P Stinis
  Advances in Neural Information Processing Systems (NeurIPS), 2021

Reduced-order Modeling

• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders [Paper] [arXiv]
  K Lee and K Carlberg
  Journal of Computational Physics (JCP), 404:108973, 2020.
  

• Deep Conservation: A latent dynamics model for exact satisfaction of physical conservation laws [Paper] [arXiv]
  K Lee and K Carlberg
  AAAI Conference on Artificial Intelligence (AAAI), 2021
  

• Parameterized neural ordinary differential equations: Applications to computational physics problems [Paper] [arXiv]
  K Lee and E Parish
  Proceedings of Royal Society A, 2021.
  

Physics-informed Neural Networks

• Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks [Preprint] [Code] W Cho, K Lee, D Rim, and N Park
  Advances in Neural Information Processing Systems (NeurIPS), 2023

• DPM: A novel training method for physics-informed neural networks in extrapolation [Paper] [arXiv]
  J Kim, K Lee, D Lee, S Y Jin, and N Park
  AAAI Conference on Artificial Intelligence (AAAI), 2021
  

Iterative Solvers for (non-)Linear Systems

• A low-rank solver for the Navier–Stokes equations with uncertain viscosity [Paper] [arXiv]
  K Lee, H C Elman, and B Sousedík
  SIAM/ASA Journal on Uncertainty Quantification (JUQ), 7(4):1275–1300, 2019.
  

• Stochastic least-squares Petrov–Galerkin method for parameterized linear systems [Paper] [arXiv]
  K Lee, K Carlberg, and H C Elman
  SIAM/ASA Journal on Uncertainty Quantification (JUQ), 6(1):374–396, 2018.
  

• A preconditioned low-rank projection method with a rank-reduction scheme for stochastic partial differential equations. [Paper] [arXiv]
  K Lee and H C Elman
  SIAM Journal on Scientific Computing (SISC), 39(5):S828–S850, 2017.