16 citations · 30 across the 4 of their papers we have counts for
3 papers · 1 filter
Physics-Informed Koopman Network
Yuying Liu, Aleksei Sholokhov, Hassan Mansour +1
Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have…
Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers
Yuying Liu, J. Nathan Kutz, Steven L. Brunton
Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized…
Multiresolution Convolutional Autoencoders
Yuying Liu, Colin Ponce, Steven L. Brunton +1
We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods…