Submitted
Second-order diffusion limit for the phonon transport equation – asymptotics and numerics
with Anjali Nair and Weiran Sun, submitted
High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville
with Shi Chen, Zhiyan Ding and Leonardo Zepeda-Nunez, submitted
On the global convergence of gradient descent for multi-layer ResNets in the mean-field regime.
with Shi Chen, Zhiyan Ding and Stephen Wright. submitted,
Unique reconstruction of the heat-reflection indices at solid interfaces
with Weiran Sun, submitted
Low rank approximation for multiscale PDEs
with Shi Chen, Ke Chen, Jianfeng Lu and Steve Wright
A reduced order Schwarz method for nonlinear miltiscale elliptic equations based on two- layer neural networks
with Shi Chen, Zhiyan Ding and Steve Wright
In Revision
Low-Dimensional Approximation to PDE Solution Manifold
with Shi Chen, Jianfeng Lu and Stephen Wright, submitted
Published
Simulating the optical properties of soot using a stochastic soot model.
with Tyler Strickland and Sage Kokjohn, SAE International Journal of Engines, 2022
Overparameterization of deep ResNet: zero loss and mean-field analysis
with Shi Chen, Zhiyan Ding and Stephen Wright. accepted, Journal of Machine Learning Research,
Bridging and improving theoretical and computational electric impedance tomography via data completion
with Leonardo Zepeda-Nunez and Tanh Bui-Thanh, accepted, SIAM-scientific computing
Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Settingwith Kathrin Hellmuth, Christian Klingenberg and Min Tang, Computation, 9(11), 2021
Bayesian inverse problem for linear and nonlinear RTE, instability in the fluid regime
with Kit Newton and Li Wang, Computation, 10(2), 2021
Constrained Ensemble Langevin Monte Carlo with Zhiyan Ding, Foundations of Data Science
Langevin Monte Carlo: random coordinate descent and variance reduction
with Zhiyan Ding, Journal of Machine Learning Research 22 (2021) 1-51
Reconstructing the thermal phonon transmission coefficient at solid interfaces in the phonon transport equation
with Irene Gamba and Anjali Nair, SIAM-Applied Math
Semi-classical limit of an inverse problem for the Schroedinger equation
with Shi Chen, accepted, Research in Mathematical Sciences
Error analysis of an asymptotic preserving dynamical low-rank integrator for the multi-scale radiative transfer equation
with Zhiyan Ding and Lukas Einkemmer, accepted, SIAM-NA
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
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
Classical limit for the varying-mass Schrödinger equation with random inhomogeneities
with Shi Chen and Xu Yang, JCP
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.
Ensemble Kalman Sampling: mean-field limit and convergence analysis
with Zhiyan Ding, SIAM J. Math. Anal.
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
Ensemble Kalman Inversion: mean-field limit and convergence analysis
with Zhiyan Ding, Stat Comput.
Reconstruction of the emission coefficient in the nonlinear radiative transfer equation.
with Ru-Yu Lai and Christian Klingenberg, SIAM J. Appl. Math.
Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds
with Zhiyan Ding, Jianfeng Lu, Foundations of Data Science
Sensitivity analysis of Burgers' equation with shocks
with Jian-Guo Liu and Ruiwen Shu, SIAM/ASA J. Uncertainty Quantification
Variance reduction for Langevin Monte Carlo in high dimensional sampling problems
with Zhiyan Ding, NeurIPS 2020 (my first conference paper!)
Structured random sketching for PDE inverse problems
with Ke Chen, Kit Newton and Stephen J. Wright, SIAM J. Matrix Anal. Appl. (my first one with the journal!)
Random Sampling and Efficient Algorithms for Multiscale PDEs
with Ke Chen, Jianfeng Lu and Stephen Wright, SIAM J. Sci. Comput.
On diffusive scaling in acousto-optic imaging
with Francis Chung and Ru-Yu Lai, Inverse Probl.
Parameter Reconstruction for general transport equation
with Ru-Yu Lai, SIAM J. Math. Anal.
Schwarz iteration method for elliptic equation with rough media based on random sampling
with Ke Chen and Stephen Wright, accepted, Proceeding, ICCM 2018
Randomized sampling for basis functions construction in generalized finite element methods
with Ke Chen, Jianfeng Lu and Stephen Wright, SIAM-Multiscale Model. Simul.
Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition
with Hongxu Chen and Chanwoo Kim, J. Stat. Phys.
Diffusive optical tomography in the Bayesian framework
with Kit Newton and Andew Stuart, 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.
Applications of Kinetic Tools to Inverse Transport Problems
with Weiran Sun, Inverse Probl.
Inverse problems for the stationary transport equation in the diffusion scaling
with Ru-Yu Lai and Gunther Uhlmann, SIAM J. Appl. Math.
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.
Numerical analysis for conservation laws using L1 minimization
with Anne Gelb and Xiao Hou, J. Sci. Comput.
Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory
with Nan Chen, Xiao Hou and Yingda Li, Atmosphere
Two-level Markov chain Monte Carlo methods for the inverse radiative transfer equation
with Kit Newton, Entropy
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.
Galerkin Method for Stationary Radiative Transfer Equations with Uncertain Coefficients
with Xinghui Zhong, J. Sci. Comput.
Stability of Stationary Inverse Transport Equation in Diffusion Scaling
with Ke Chen and Li Wang, Inverse Probl.
Uniform regularity for linear kinetic equations with random input based on hypocoercivity
with Li Wang, SIAM/ASA J. Uncertainty Quantification
An asymptotic preserving method for transport equations with oscillatory scattering coefficients
with Jianfeng Lu, SIAM-Multiscale Model. Simul.
On quantifying uncertainties for the linearized BGK kinetic equation
with Christian Klingenberg and Marlies Pirner, Proc. 16th Int’l Conf. on Hyperbolic Problems
A convergent method for linear half-space kinetic equations
with Jianfeng Lu and Weiran Sun, finally appeared, ESAIM: M2AN
Implicit Asymptotic Preserving Method for Linear Transport Equations
with Li Wang, Commun. Comput. Phys.
Half-space Kinetic Equations with General Boundary Conditions
with Jianfeng Lu and Weiran Sun, Math Comp
A sparse decomposition of low rank symmetric positive semi-definite matrices
with Thomas Y. Hou and Pengchuan Zhang, SIAM-Multiscale Model. Simul.
Exploring the locally low dimensional structure in solving random elliptic PDEs
with Thomas Y. Hou and Pengchuan Zhang, SIAM-Multiscale Model. Simul.
Validity and regularization of classical half-space equations
with Jianfeng Lu and Weiran Sun, J. Stat. Phys.
Sparse+Low-energy decomposition for viscous conservation laws
with Thomas Y. Hou and Hayden Schaeffer, J. Comput. Phys.
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.
Diffusion approximations of linear transport equations: asymptotics and numerics
with Jianfeng Lu and Weiran Sun, J. Comput. Phys.
Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy
with Jingwei Hu and Lorenzo Pareschi, J. Sci. Comput.
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.
Semiclassical models for Schrodinger equations with periodic potentials and band-crossings
with Lihui Chai and Shi Jin, Kinet. Relat. Models
A BGK-penalization based asymptotic-preserving scheme for the multi-species Boltzmann equation
with: Shi Jin, Numer. Methods Partial Differential Equations
Book chapters
Numerical methods for plasma physics in collisional regimes
with Giacomo Dimarco, Lorenzo Pareschi and Bokai Yan, review article, J. Plasma Physics
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
Thesis
Modeling and Computational Methods for Multi-scale Quantum Dynamics and Kinetic Equations
