447 citations · 733 across the 44 of their papers we have counts for
5 papers · 1 filter
High-dimensional Optimal Density Control with Wasserstein Metric Matching
Shaojun Ma, Mengxue Hou, Xiaojing Ye +1
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable age…
Parameterized Wasserstein Hamiltonian Flow
Hao Wu, Shu Liu, Xiaojing Ye +1
In this work, we propose a numerical method to compute the Wasserstein Hamiltonian flow (WHF), which is a Hamiltonian system on the probability density manifold. Many well-known PD…
RRCNN: A novel signal decomposition approach based on recurrent residue convolutional neural network
Feng Zhou, Antonio Cicone, Haomin Zhou
The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decompositio…
Why Shallow Networks Struggle to Approximate and Learn High Frequencies
Shijun Zhang, Hongkai Zhao, Yimin Zhong +1
In this work, we present a comprehensive study combining mathematical and computational analysis to explain why a two-layer neural network struggles to handle high frequencies in b…
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Nathan Gaby, Xiaojing Ye, Haomin Zhou
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order mode…