**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 Dynamics*, University 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***.**