4 citations · 6 across the 4 of their papers we have counts for
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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…
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…
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.…
Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs
Shi Jin, Liu Liu, Giovanni Russo +1
In this work, we study the semi-classical limit of the Schrödinger equation with random inputs, and show that the semi-classical Schrödinger equation produces osci…
Asymptotic-preserving schemes for two-species binary collisional kinetic system with disparate masses I: time discretization and asymptotic analysis
Irene M. Gamba, Shi Jin, Liu Liu
We develop efficient asymptotic-preserving time discretization schemes to solve the disparate mass kinetic system of a binary gas or plasma in the "relaxation time scale" relevant…