Qin Li

Numerical methods in general settings:

• Inverse problems and sampling
  Overparameterization of deep ResNet: zero loss and mean-field analysis
  with Shi Chen, Zhiyan Ding and Stephen Wright. submitted,
  
  Bridging and improving theoretical and computational electric impedance tomography via data completion
  with Leonardo Zepeda-Nunez and Tanh Bui-Thanh, submitted
  
  Langevin Monte Carlo: random coordinate descent and variance reduction
  with Zhiyan Ding, submitted
  
  Random Coordinate Langevin Monte Carlo
  with Zhiyan Ding, Jianfeng Lu and Stephen Wright, COLT, 2021
  
  Random Coordinate Underdamped Langevin Monte Carlo
  with Zhiyan Ding, Jianfeng Lu and Stephen Wright, AISTATS, 2021
  
  Variance reduction for Langevin Monte Carlo in high dimensional sampling problems
  with Zhiyan Ding, NeurIPS 2020
  
  Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds
  with Zhiyan Ding, Jianfeng Lu, Foundations of Data Science
  
  Ensemble Kalman Sampling: mean-field limit and convergence analysis
  with Zhiyan Ding, SIAM J. Math. Anal.
  
  Ensemble Kalman Inversion: mean-field limit and convergence analysis
  with Zhiyan Ding, Stat Comput.
  
  Structured random sketching for PDE inverse problems
  with Ke Chen, Kit Newton and Stephen J. Wright, SIAM J. Matrix Anal. Appl.
  
  Error lower bounds of constant step-size stochastic gradient descent
  with Yiding Chen, Zhiyan Ding, and Jerry Zhu, rejected
  
  
• Low rank structure of hyperbolic systems
  Sparse+Low-energy decomposition for viscous conservation laws
  with Thomas Y. Hou and Hayden Schaeffer, J. Comput. Phys.
  
  Numerical analysis for conservation laws using L1 minimization
  with Anne Gelb and Xiao Hou, J. Sci. Comput.
  
  
• Low rank structure of elliptic equations
  Randomized sampling for basis functions construction in generalized finite element methods
  with Ke Chen, Jianfeng Lu and Stephen Wright, SIAM-Multiscale Model. Simul.
  
  Random Sampling and Efficient Algorithms for Multiscale PDEs
  with Ke Chen, Jianfeng Lu and Stephen Wright, SISC, accepted
  
  A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient
  with Ke Chen, Jianfeng Lu and Stephen Wright, SIAM-Multiscale Model. Simul.
  
  Low-Dimensional Approximation to PDE Solution Manifold
  with Shi Chen, Jianfeng Lu and Stephen Wright, submitted
  
  Schwarz iteration method for elliptic equation with rough media based on random sampling
  with Ke Chen and Stephen Wright, accepted, Proceeding, ICCM 2018
  
  

Uncertainties

• Elliptic type
  Exploring the locally low dimensional structure in solving random elliptic PDEs
  with Thomas Y. Hou and Pengchuan Zhang, SIAM-Multiscale Model. Simul.
  
  A sparse decomposition of low rank symmetric positive semi-definite matrices
  with Thomas Y. Hou and Pengchuan Zhang, SIAM-Multiscale Model. Simul.
  
  
• Hyperbolic type
  Uniform regularity for linear kinetic equations with random input based on hypocoercivity
  with Li Wang, SIAM/ASA J. Uncertainty Quantification
  
  Galerkin Method for Stationary Radiative Transfer Equations with Uncertain Coefficients
  with Xinghui Zhong, J. Sci. Comput.
  
  On quantifying uncertainties for the linearized BGK kinetic equation
  with Christian Klingenberg and Marlies Pirner, Proc. 16th Int’l Conf. on Hyperbolic Problems
  
  Sensitivity analysis of Burgers' equation with shocks
  with Jian-Guo Liu and Ruiwen Shu, accepted, SIAM/ASA J. Uncertainty Quantification
  
  
• Information Theory
  Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory
  with Nan Chen, Xiao Hou and Yingda Li, Atmosphere
  
  State-specific Projection of COVID-19 Infection in the United States and Evaluation of Three Major Control Measures
  with Shi Chen, Song Gao, Yuhao Kang and Xun Shi, Scientific Reports
  
  Intra-county modeling of COVID-19 infection with human mobility: assessing spatial heterogeneity with business traffic, age and race
  with Xiao Hou, Song Gao, Nan Chen, Kaiping Chen, Yuhao Kang, Jingmeng Rao, Jordan Ellenberg and Jonathan Patz, PNAS
  
  

Kinetic theory

• Boundary layer analysis
  A convergent method for linear half-space kinetic equations
  with Jianfeng Lu and Weiran Sun, finally appeared, ESAIM: M2AN
  
  Half-space Kinetic Equations with General Boundary Conditions
  with Jianfeng Lu and Weiran Sun, Math Comp
  
  Diffusion approximations of linear transport equations: asymptotics and numerics
  with Jianfeng Lu and Weiran Sun, J. Comput. Phys.
  
  Validity and regularization of classical half-space equations
  with Jianfeng Lu and Weiran Sun, J. Stat. Phys.
  
  A numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer
  with Hongxu Chen and Jianfeng Lu, J. Comput. Phys.
  
  Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition
  with Hongxu Chen and Chanwoo Kim, J. Stat. Phys.
  
  
• Inverse problems
  Stability of Stationary Inverse Transport Equation in Diffusion Scaling
  with Ke Chen and Li Wang, Inverse Probl.
  
  A numerical approach to inverse transport equation with error analysis
  with Ruiwen Shu and Li Wang, SIAM J. Numer. Anal.
  
  Stability of Inverse Transport Equation in Diffusion Scaling and Fokker-Planck limit
  with Ke Chen and Li Wang, SIAM J. Appl. Math.
  
  Online learning in optical tomography: a stochastic approach
  with Ke Chen and Jian-Guo Liu, Inverse Probl.
  
  Inverse problems for the stationary transport equation in the diffusion scaling
  with Ru-Yu Lai and Gunther Uhlmann, SIAM J. Appl. Math.
  
  Parameter Reconstruction for general transport equation
  with Ru-Yu Lai, SIAM J. Math. Anal.
  
  Two-level Markov chain Monte Carlo methods for the inverse radiative transfer equation
  with Kit Newton, Entropy
  
  Diffusive optical tomography in the Bayesian framework
  with Kit Newton and Andrew Stuart, SIAM-Multiscale Model. Simul.
  
  Applications of Kinetic Tools to Inverse Transport Problems
  with Weiran Sun, Inverse Probl.
  
  On diffusive scaling in acousto-optic imaging
  with Francis Chung and Ru-Yu Lai, Inverse Probl.
  
  Reconstruction of the emission coefficient in the nonlinear radiative transfer equation.
  with Ru-Yu Lai and Christian Klingenberg, SIAM J. Appl. Math.
  
  Reconstructing the thermal phonon transmission coefficient at solid interfaces in the phonon transport equation
  with Irene Gamba and Anjali Nair, submitted
  
  Unique reconstruction of the heat-reflection indices at solid interfaces
  with Weiran Sun, submitted
  
  
• Homogenization
  An asymptotic preserving method for transport equations with oscillatory scattering coefficients
  with Jianfeng Lu, SIAM-Multiscale Model. Simul.
  
  Generalized multiscale finite element method for the steady state linear Boltzmann equation
  with Eric Chung, Yalchin Efendiev and Yanbo Li, SIAM-Multiscale Model. Simul.
  
  
• Asymptotic preserving methods
  A BGK-penalization based asymptotic-preserving scheme for the multi-species Boltzmann equation
  with: Shi Jin, Numer. Methods Partial Differential Equations
  
  Exponential Runge–Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
  with Lorenzo Pareschi, J. Comput. Phys.
  
  Exponential Runge-Kutta based AP scheme for multi-species Boltzmann equation
  with Xu Yang, Commun. Comput. Phys.
  
  Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy
  with Jingwei Hu and Lorenzo Pareschi, J. Sci. Comput.
  
  Numerical methods for plasma physics in collisional regimes
  with Giacomo Dimarco, Lorenzo Pareschi and Bokai Yan, review article, J. Plasma Physics
  
  Implicit Asymptotic Preserving Method for Linear Transport Equations
  with Li Wang, Commun. Comput. Phys.
  
  Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations" for the book "Handbook on Numerical Methods for Hyperbolic Problems
  with Jingwei Hu and Shi Jin, review article, Handbook on Numerical Methods for Hyperbolic Problems
  
  Error analysis of an asymptotic preserving dynamical low-rank integrator for the multi-scale radiative transfer equation
  with Zhiyan Ding and Lukas Einkemmer, submitted
  
  

Quantum system with crossing energies

• semi-classical limit
  Semiclassical models for Schrodinger equations with periodic potentials and band-crossings
  with Lihui Chai and Shi Jin, Kinet. Relat. Models
  
  Semiclassical model for the surface hopping problem, multiband Wigner approach and domain decomposition method
  with Lihui Chai, Shi Jin and Omar Morandi, SIAM-Multiscale Model. Simul.
  
  Classical limit for the varying-mass Schrödinger equation with random inhomogeneities
  with Shi Chen and Xu Yang, JCP
  
  
• inverse problems
  Semi-classical limit of an inverse problem for the Schroedinger equation
  with Shi Chen, accepted
  
  

Thesis:

Modeling and Computational Methods for Multi-scale Quantum Dynamics and Kinetic Equations