16 citations · 30 across the 4 of their papers we have counts for
4 papers
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…
A relaxation accelerated two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems
Dongkai Li, Li Wang, Yuying Liu
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method…
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…