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Welcome to LIU Liu’s Homepage!

 



I am currently an Assistant Professor at Department of Mathematics of The Chinese University of Hong Kong. 

 

 

Research Interests: My research interest focuses on applied numerical analysis and scientific computation. I have conducted research in kinetic theory, uncertainty quantification, quantum dynamics, data-driven science, developed efficient numerical schemes for complex multiscale problems and model reduction methods for high-dimensional problems.


Education: I earned my doctorate degree of Mathematics at University of Wisconsin-Madison (2012-2017). Prior to that, I received the Bachelor degree (First Honour) in Applied and Computational Mathematics at Hong Kong Baptist University (2008-2012). 


Working Experience: Before joining CUHK in summer 2020, I was a Peter O'Donnell, Jr. Postdoc and instructor at Oden ICES and Department of Mathematics of University of Texas at Austin from 2017-2020. 

 


Fundings and Awards: 

•  Early Career Scheme (24301021) awarded by Research Grants Council of Hong Kong, 2021 (PI)

•  Direct Grants (171365642), Research Committee of CUHK, 2021 (PI)

•  National Key R&D Program of China (2021YFA1001200), Ministry of Science and Technology, China, 2021 (co-PI)

•  General Research Fund (No. 14303022), Research Grants Council of Hong Kong, 2022 (PI)

•  General Research Fund (No. 14301423), Research Grants Council of Hong Kong, 2023 (PI)

 

Publications: 

Refereed Journals: 

•   Shi Jin, Liu Liu, An Asymptotic-Preserving Stochastic Galerkin Method for the Semiconductor Boltzmann Equation with Random Inputs and Diffusive Scalings, SIAM Multiscale Modeling and Simulation, 15 (1), 157-183, 2017.


•   Zheng Chen, Liu Liu, Lin Mu, DG-IMEX Stochastic Galerkin schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings, Journal of Scientific Computing (a special issue in honor of the 60th birthday of Chi Wang Shu), 73 (2), 566-592, 2017.


•   Liu Liu, Uniform Spectral Convergence of the Stochastic Galerkin Method for the Linear Semiconductor Boltzmann Equation with Random Inputs and Diffusive Scalings, Kinetic and Related Models, 11 (5), 1139-1156, 2018.


•   Liu Liu, Uncertainty Quantification for Multiscale Kinetic Equations and Quantum DynamicsUniversity of Wisconsin-Madison, 2017. 


•   Liu Liu, Shi Jin, Hypocoercivity based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs, SIAM Multiscale Modeling and Simulation, 16 (3), 1085-1114, 2018.


•   Liu Liu, A Stochastic Asymptotic-preserving Scheme for the Bipolar Semiconductor Boltzmann- Poisson System with Random Inputs and Diffusive Scalings, Journal of Computational Physics, 376, 634-659, 2019.


•   Irene M. Gamba, Shi Jin, Liu Liu, Micro-macro Decomposition based Asymptotic-preserving Numerical Schemes and Numerical Moment Conservations for Collisional Nonlinear Kinetic Equations, Journal of Computational Physics, 382, 264-290, 2019.


•   Liu Liu, Marlies Pirner, Hypocoercivity for a BGK Model for Gas Mixtures, Journal of Differential Equations, 267, 119-149, 2019. 


•   Esther S. Daus, Shi Jin, Liu Liu, Spectral Convergence of the Stochastic Galerkin Approximation to the Boltzmann Equation with Multiple Scales and Large Random Perturbation in the Collision Kernel, Kinetic and Related Models, 12(4), 909-922, 2019.


•   Irene M. Gamba, Shi Jin, Liu Liu, Asymptotic-preserving Schemes for Two-species Binary Collisional Kinetic System with Disparate Masses I: Time Discretization and Asymptotic Analysis, Comm. Math. Sci. (a special issue in memory of David Cai), 17(5), 1257-1289, 2019. 


•   Shi Jin, Liu Liu, Giovanni Russo, Zhennan Zhou, Gaussian Wave Packet Transform based Numerical Scheme for the Semiclassical Schrödinger Equation with Random Inputs, Journal of Computational Physics, 401, 109015, 2020. 


•  Liu Liu, Xueyu Zhu, A Bi-fidelity Method for the Boltzmann Equation with Random Parameters and Multiple Scales, Journal of Computational Physics, 402, 108914, 2020. 


•  Nicolas Crouseilles, Shi Jin, Liu Liu, Mohammed Lemou, Nonlinear Geometric Optics Based Multiscale Stochastic Galerkin Methods for Highly Oscillatory Transport Equations with Random Inputs, ESAIM. Mathematical Modelling and Numerical Analysis, 54(6), 1849-1882, 2020.  


•  Irene M. Gamba, Shi Jin, Liu Liu, Error Estimate of the Bi-fidelity Method for Kinetic Equations with Random Parameters and Different Scalings, International Journal for Uncertainty Quantification, 11, 57-75, 2021.


•  Esther S. Daus, Shi Jin, Liu Liu, On the Multi-species Boltzmann Equation with Uncertainty and its Stochastic Galerkin Approximation, ESAIM: Mathematical Modelling and Numerical Analysis, 55, 1323-1345, 2021.


•  Zheng Chen, Liu Liu, Lin Mu, Solving the Linear Transport Equation by a Deep Neural Network Approach, Discrete and Continuous Dynamical Systems, Series S, 15 (4), 669-686, 2022.


•  Liu Liu, Lorenzo Pareschi, Xueyu Zhu, A Bi-fidelity Stochastic Collocation Method for Transport Equations with Diffusive Scaling and Multi-dimensional Random Inputs, Journal of Computational Physics, 462, 111252, 2022.


•  Guilia Bertaglia, Liu Liu, Lorenzo Pareschi, Xueyu Zhu, Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties, Networks and Heterogeneous Media, 17 (3), 2022.


•  Giacomo Dimarco, Liu Liu, Lorenzo Pareschi, Xueyu Zhu, Multi-fidelity methods for uncertainty propagation in kinetic equations, Panoramas & Synthèses, Société Mathématique de France, 2022.


•  Liu Liu, A study of multiscale kinetic models with uncertainties, Book chapter of SEMA SIMAI Springer Series, Springer, 2023.


•  Yating Wang, Liu Liu, On a neural network approach for solving potential control problem of the semiclassical Schrödinger equation, Journal of Computational and Applied Mathematics 438(5):115504, 2023.


•  Yu Feng, Liu Liu, Zhennan Zhou, A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws, ESAIM: Mathematical Modelling and Numerical Analysis,   58 (2): 613-638, 2024.


•  Liu Liu, Kunlun Qi, Stability and convergence of the gPC-Galerkin Fourier spectral method for the Boltzmann equation with uncertainties, Communications in Mathematical Sciences, to appear.


•  Liu Liu, Kunlun Qi, Spectral convergence of a semi-discretized numerical system for the Boltzmann equation with uncertainties, SIAM Journal on Uncertainty Quantification, to appear.


• Yiwen Lin, Liu Liu, On a class of multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties, preprint.

 

 Conference Proceedings: 

•  Liu Liu, A Bi-fidelity DG-IMEX Method for the Linear Transport Equation with Random Parameters, 14th World Congress on Computational Mechanics (WCCM) ECCOMAS Congress, 2020.


For students and postdocs who are interested in working with me, you are welcome to contact me at lliu@math.cuhk.edu.hk.


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