10 citations · 29 across the 6 of their papers we have counts for
8 papers
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…
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…
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…