4 citations · 6 across the 4 of their papers we have counts for
10 papers
Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs
Cheng Chang, Liu Liu, Tieyong Zeng
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving…
A deep neural network approach on solving the linear transport model under diffusive scaling
Liu Liu, Tieyong Zeng, Zecheng Zhang
In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is c…
Robust Structured Statistical Estimation via Conditional Gradient Type Methods
Jiacheng Zhuo, Liu Liu, Constantine Caramanis
Structured statistical estimation problems are often solved by Conditional Gradient (CG) type methods to avoid the computationally expensive projection operation. However, the exis…
Error estimate of a bi-fidelity method for kinetic equations with random parameters and multiple scales
Irene M. Gamba, Shi Jin, Liu Liu
In this paper, we conduct uniform error estimates of the bi-fidelity method for multi-scale kinetic equations. We take the Boltzmann and the linear transport equations as important…
NODE: Extreme Low Light Raw Image Denoising using a Noise Decomposition Network
Hao Guan, Liu Liu, Sean Moran +2
Denoising extreme low light images is a challenging task due to the high noise level. When the illumination is low, digital cameras increase the ISO (electronic gain) to amplify th…
A bi-fidelity method for the multiscale Boltzmann equation with random parameters
Liu Liu, Xueyu Zhu
In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C.…