20 citations · 87 across the 20 of their papers we have counts for
20 papers
A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws
Yu Feng, Liu Liu, Zhennan Zhou
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The mode…
Robust Imitation Learning from Corrupted Demonstrations
Liu Liu, Ziyang Tang, Lanqing Li +1
We consider offline Imitation Learning from corrupted demonstrations where a constant fraction of data can be noise or even arbitrary outliers. Classical approaches such as Behavio…
Multi-fidelity methods for uncertainty propagation in kinetic equations
Giacomo Dimarco, Liu Liu, Lorenzo Pareschi +1
The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computation…
Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
Giulia Bertaglia, Liu Liu, Lorenzo Pareschi +1
Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertain…
A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs
Liu Liu, Lorenzo Pareschi, Xueyu Zhu
In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the pr…
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…
On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation
Esther S. Daus, Shi Jin, Liu Liu
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time beha…
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…
Spectral Convergence of the Stochastic Galerkin Approximation to the Boltzmann Equation with Multiple Scales and Large Random Perturbation in the Collision Kernel
Esther S. Daus, Shi Jin, Liu Liu
In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the sto…
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…
Hypocoercivity for a BGK model for gas mixtures
Liu Liu, Marlies Pirner
We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continu…
Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations
Irene M. Gamba, Shi Jin, Liu Liu
In this paper, we first extend the micro-macro decomposition method for multiscale kinetic equations from the BGK model to general collisional kinetic equations, including the Bolt…
Hypocoercivity based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs
Liu Liu, Shi Jin
In this paper, we provide a general framework to study general class of linear and nonlinear kinetic equations with random uncertainties from the initial data or collision kernels,…
Uniform Spectral Convergence of the Stochastic Galerkin Method for the Linear Semiconductor Boltzmann Equation with Random Inputs and Diffusive Scalings
Liu Liu
In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin method for the linear semiconductor Boltzmann equation under diffusive scaling and with ran…
Nonlinear Geometric Optics Based Multiscale Stochastic Galerkin Methods for Highly Oscillatory Transport Equations with Random Inputs
Nicolas Crouseilles, Shi Jin, Mohammed Lemou +1
We develop generalized polynomial chaos (gPC) based stochastic Galerkin (SG) methods for a class of highly oscillatory transport equations that arise in semiclassical modeling of n…