53 citations · 149 across the 23 of their papers we have counts for
25 papers
Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks
Woojin Cho, Kookjin Lee, Donsub Rim +1
In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (…
Reversible and irreversible bracket-based dynamics for deep graph neural networks
Anthony Gruber, Kookjin Lee, Nathaniel Trask
Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, how…
Time Series Forecasting with Hypernetworks Generating Parameters in Advance
Jaehoon Lee, Chan Kim, Gyumin Lee +6
Forecasting future outcomes from recent time series data is not easy, especially when the future data are different from the past (i.e. time series are under temporal drifts). Exis…
Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecasting
Fan Wu, Sanghyun Hong, Donsub Rim +2
Continuous-time dynamics models, such as neural ordinary differential equations, have enabled the modeling of underlying dynamics in time-series data and accurate forecasting. Howe…
Not All Asians are the Same: A Disaggregated Approach to Identifying Anti-Asian Racism in Social Media
Fan Wu, Sanyam Lakhanpal, Qian Li +4
Recent policy initiatives have acknowledged the importance of disaggregating data pertaining to diverse Asian ethnic communities to gain a more comprehensive understanding of their…
Parameter-varying neural ordinary differential equations with partition-of-unity networks
Kookjin Lee, Nathaniel Trask
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (PO…
AdamNODEs: When Neural ODE Meets Adaptive Moment Estimation
Suneghyeon Cho, Sanghyun Hong, Kookjin Lee +1
Recent work by Xia et al. leveraged the continuous-limit of the classical momentum accelerated gradient descent and proposed heavy-ball neural ODEs. While this model offers computa…
Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
Bedřich Sousedík, Kookjin Lee
We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model p…
Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery
Nathaniel Trask, Carianne Martinez, Kookjin Lee +1
We introduce physics-informed multimodal autoencoders (PIMA) - a variational inference framework for discovering shared information in multimodal scientific datasets representative…
Calibrating hypersonic turbulence flow models with the HIFiRE-1 experiment using data-driven machine-learned models
Kenny Chowdhary, Chi Hoang, Kookjin Lee +1
In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationa…
Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
Kookjin Lee, Nathaniel Trask, Panos Stinis
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved…
Probabilistic partition of unity networks: clustering based deep approximation
Nat Trask, Mamikon Gulian, Andy Huang +1
Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of trainin…
Machine learning structure preserving brackets for forecasting irreversible processes
Kookjin Lee, Nathaniel A. Trask, Panos Stinis
Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve st…
Projection-based model reduction of dynamical systems using space-time subspace and machine learning
Chi Hoang, Kenny Chowdhary, Kookjin Lee +1
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output qua…
Partition of unity networks: deep hp-approximation
Kookjin Lee, Nathaniel A. Trask, Ravi G. Patel +2
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity…
DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation
Jungeun Kim, Kookjin Lee, Dongeun Lee +2
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in…
Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems
Kookjin Lee, Eric J. Parish
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to…
Deep Conservation: A latent-dynamics model for exact satisfaction of physical conservation laws
Kookjin Lee, Kevin Carlberg
This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimen…
Solving Large-Scale 0-1 Knapsack Problems and its Application to Point Cloud Resampling
Duanshun Li, Jing Liu, Noseong Park +7
0-1 knapsack is of fundamental importance in computer science, business, operations research, etc. In this paper, we present a deep learning technique-based method to solve large-s…
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
Kookjin Lee, Kevin Carlberg
Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such a…
Inexact Methods for Symmetric Stochastic Eigenvalue Problems
Kookjin Lee, Bedřich Sousedík
We study two inexact methods for solutions of random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetri…
A Low-rank solver for the Navier--Stokes equations with uncertain viscosity
Kookjin Lee, Howard C. Elman, Bedřich Sousedík
We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linear…
MMGAN: Manifold Matching Generative Adversarial Network
Noseong Park, Ankesh Anand, Joel Ruben Antony Moniz +5
It is well-known that GANs are difficult to train, and several different techniques have been proposed in order to stabilize their training. In this paper, we propose a novel train…
Stochastic Least-Squares Petrov-Galerkin Method for Parameterized Linear Systems
Kookjin Lee, Kevin Carlberg, Howard C. Elman
We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input para…