53 citations · 149 across the 23 of their papers we have counts for
6 papers · 1 filter
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…