Last update Sep 16, 2021.  

Manuscripts in preparation:

A. Submitted and Published journal papers:
  1. Wenhao He, Tongyang Li, Xiantao Li Zecheng Li, Chunhao Wang and Ke Wang, Efficient Optimal Control of Open Quantum Systems, TQC, Accepted, 2024.

  2. Zhiyan Ding, Xiantao Li and Lin Lin, Simulating Open Quantum Systems Using Hamiltonian Simulations, PRX Quantum, Accepted, 2024.

  3. Zhiyan Ding, Taehee Ko, Jiahao Yao, Lin Lin, and Xiantao Li, Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits, Preprint, 2023.

  4. Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi, Chunhao Wang, Stochastic Quantum Sampling for Non-Logconcave Distributions and Estimating Partition Functions, Preprint, 2023.

  5. With Taehee Ko and Chunhao Wang, Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms, Preprint, 2023.

  6. With Ke Wang, Simulation-assisted learning of open quantum systems, Preprint, 2023.

  1. With Jin, Liu, Yu, Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions., Journal of Computational Physics, Vol 498, 112707, 2024.

  2. With Jin, Liu, Yu, Quantum Simulation for Quantum Dynamics with Artificial Boundary Condition, SIAM Journal on Scientific Computing, Accepted, 2024.

  3. With C. Wang, Efficient Quantum Algorithms for Quantum Optimal Control, ICML, 2023.

  4. With C. Wang, Efficient Simulating Markovian open quantum systems using higher-order series expansion, ICALP, 2023.

  5. Enabling Quantum Speedup of Markov Chains using a Multi-level Approach, Preprint, 2022.

  6. With Venturi, The Mori-Zwanzig formulation of deep learning, Research in the Mathematical Sciences, Vol 10, 23, 2023.

  1. With Luo and Hao, Stability Preserving Data-driven Models With Latent Dynamics, Chaos, Vol 32, 081103 2022.

  2. With Taehee Ko, A Local Convergence Theory for the Stochastic Gradient Descent Method in Non-Convex Optimization With Non-isolated Local Minima, Journal Machine Learning, Vol 2, 138-160, 2023.

  3. With S. Jin and Nana Liu, Hamiltonian Simulation in the semi-classical regime Quantum, Vol 6, pp 739, 2022.

  4. X Li, Some Error Analysis for the Quantum Phase Estimation Algorithms Journal of Physics A: Mathematical and Theoretical, 2022.

  5. With Chunhao Wang, Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems Communications in Mathematical Physics, , Vol 401, pages 147–183 2023.

  6. With Shi Jin, A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations, Communications on Applied Mathematics and Computation, 2023.

  1. With Taehee Ko, Stochastic Algorithms for Self-consistent Calculations of Electronic Structures , Mathematics of Computation, Vol 92, 1693-1728, 2023.

  2. With Chu, A Projection-based Reduced-order Method for Electron Transport Problems with Long-range Interactions , Journal of Chemical Physics, Volume 155, page 114105, 2021.

  3. With Zhang and Harlim, Error Bounds of the Invariant Statistics in Machine Learning of Ergodic It\^o Diffusions, Physica D, Volume 427, page 133022, 2021.

  4. With Luo and Hao, Projection based model reduction for the immersed boundary method, International Journal for Numerical Methods in Biomedical Engineering, 2021.

  5. With Xie and Chen, A machine-learning method for time-dependent wave equations over unbounded domains, preprint, 2021.

  6. H. Lei and X. Li, Petrov-Galerkin methods for the construction of non-Markovian dynamics preserving nonlocal statistics, Journal of Chemical Physics, 154, 184108 (2021).

  1. With S. Jin, Random Batch Algorithms for Quantum Monte Carlo simulations, Communications in Computational Physics, Vol 28, 1907-1936, 2020.

  2. X. Li, On Markovian Embedding Procedures for the Non-Markovian Stochastic Schrodinger Equation, Physics Letters A, Vol 387, 127036, 2021.

  1. With Q Du and L. Yuan, Analysis of coarse-grained lattice models and connections to nonlocal interactions, CSIAM Trans. Appl. Math, 2020.

  2. With H Zhang and J Harlim, Estimating linear response statistics using orthogonal polynomial based estimators: An RKHS formulation, Foundation of Data Science, Vol 2, 443-485, 2020.

  3. With Francesca Grogan, H Lei, and N A Baker, Data-driven molecular modeling with the generalized Langevin equation Journal of Computational Physics, 2020.

  4. With W. Chu, A reduced-order modeling approach for electron transport in molecular junctions, J. Chem. Theory Comput, 2020.

  5. With H. Zhang and J. Harlim, Linear Response Based Parameter Estimation in the Presence of Model Error, J Computational Physics, 2020.

  1. With Jingze Li, Exponential Integrators for Stochastic Schrödinger Equation, Physical Review E, 2020.

  2. With Xiaojie Wu, Absorbing boundary conditions for the time-dependent Schrodinger-type equations in R^3, Physical Review E, Vol 101, 013304, 2020. Link to the paper

  3. X. Li, The Computation of Local Stress in ab initio Molecular Simulations, Modelling Simul. Mater. Sci. Eng, 27 065016, 2019. Link to the paper

  4. X. Li, Absorbing Boundary Conditions for Time-dependent Schr\"{o}dinger equations: A Density-matrix Formulation, Journal of Chemical Physics, (150) 114111, 2019. Link to the paper

  5. With W. Chu, Nonlinear Constitutive Models for Nano-scale Heat Conduction, SIAM MMS, Volume 19, 533-549, 2021.

  6. With L Ma and C Liu, Coarse-graining Langevin dynamics using reduced-order techniques, Journal of Computational Physics, (380) 170-190, 2019. Link to the paper

  7. With Zhand and Harlim, A Parameter Estimation Method Using Linear Response Statistics: Numerical Scheme, Chaos, Vol 29, 033101, 2019.

  8. With Weiqi Chu, The Mori-Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics, Communications in Mathemathical Sciences, Vol. 17, 539 -- 563, 2019.

  9. With Xiaojie Wu, Stable absorbing boundary conditions for molecular dynamics in general domains, Computational Mechanics (2018). https://doi.org/10.1007/s00466-018-1562-0.

  10. With Weiqi Chu, On the asymptotic behavior of the kernel function of the Generalized Langevin equation -- a one-dimensional lattice model. J. Statistical Physics, Vol. 170, page 378, 2018.

  11. With Adam Telatovich, The strong convergence of operator-splitting methods for the Langevin dynamics model, submitted, arXiv:1706.04237, 2018.

  12. With J. Harlim and H. Zhang, A Parameter Estimation Method Using Linear Response Statistics, Journal of Statistical Physics, Vol 168, 146-170, 2017.

  13. With L Ma and C Liu, Fluctuation-Dissipation Theorem Consistent Approximation of the Langevin Dynamics Model, Comm. Math. Sci., Vol 15, 1171-1181, 2017.

  14. With L Lin and J Lu, PEXSI-$\Sigma$: A Green's function embedding method for Kohn-Sham density functional theory, Annals of Mathematical Sciences and Applications, Vol. 3, No. 2 (2018), pp. 441-472.

  15. With H Lei and N Baker, Data-driven parameterization of the generalized Langevin equation, Proc. Natl. Acad. Sci., 1609587113, 2016.

  16. With L. Ma and C. Liu, From Generalized Langevin Equations to Brownian Dynamics and Embedded Brownian Dynamics, Journal of Chemical Physics, Vol 145, 114102, 2016.

  17. With L. Ma and C. Liu, Derivation and approximation of coarse-grained dynamics from Langevin dynamics, Journal of Chemical Physics, 145, 204117 (2016).

  18. With Xiaojie Wu, Simulations of Micron-scale Fracture using Atomistic-based Boundary Element Method, Modelling and Simulation in Materials Science and Engineering, Vol 25, 085008, 2017.

  19. With Zhen Li, Xin Bian, and George Em Karniadakis, Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism , Journal of Chemical Physics, 143, 243128 (2015).

  20. With Jerry Z Yang, and Cheng Yuan, An effective and easy-to-implement boundary condition for molecular dynamics simulations, Communications in Computational Physics, 26 (2019), pp. 192-205.

  21. With L Wu and G Lin, The Mori-Zwanzig formalism for coarse-graining molecular dynamics models: A quasi-harmonic approximation, submitted.

  22. With Jianfeng Lu, Traction Boundary Conditions for Molecular Static Simulations, Computer Methods in Applied Mechanics and Engineering, Vol 308, 310--329, 2016.

  23. With J. Harlim, Parametric reduced models for the nonlinear Schrodinger equation, Physical Review E, 91, 053306.

  24. With C. Liang and X. Yuan, Some New Symplectic Multiple Timestepping Methods for Multiscale Molecular Dynamics Models, submitted.

  25. With Jingrun Chen and Carlos García-Cervera, An atomistic/continuum coupling method using enriched bases, Multiscale Modeling and Simulations, 13, 766-789, 2015.

  1. Heat conduction in nanoscale materials: A statistical-mechanics derivation of the local heat flux, Physical Review E, 90 032112 (2014) .

  2. With Xiaojie Wu, On Consistent Definitions of Momentum and Energy Fluxes for Molecular Dynamics Models with Multi-body Interatomic Potentials, Modelling and Simulation in Materials Science and Engineering, 23, 015003, 2015.

  3. With M. Chen and C. Liu, Computation of the Memory Functions in the Generalized Langevin Models for Collective Dynamics of Macromolecules, J. Chemical Physics, Vol 141 064112, 2014.

  4. A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory, J. Appl. Phys.. (116), 164314 (2014).



  1. With P. Ming, A study on the quasiconinuum approximations of a one-dimensional fracture model, SIAM Multiscale Modeling and Simulation, 12, 1379-1400, 2014.

  2. With J.Z. Yang, C. Mao and C. Liu, On the Cauchy-Born Approximation at Finite Temperature, Computational Materials Science, 99, 21-28, 2015.

  3. With J.Z. Yang and X. Wu, Accurate Evaluations of Strain and Stress in Atomistic Simulations of Crystalline Solids, Modelling and Simulation in Materials Science and Engineering, 22, Page 045008, 2014.

  4. X. Li, Boundary condition for molecular dynamics models of solids: A variational formulation based on lattice Green's functions, submitted.



  1. X. Li, Coarse-graining molecular dynamics models using an extended Galerkin projection, International Journal for Numerical Methods in Engineering, Vol 99, pages 157--182, 2014.

  2. X. Li and P. Ming, On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension, Commun. Comput. Phys., 15 (2014), pp. 647-676.

  3. X. Li, A Bifurcation Study of Crack Initiation and Kinking, The European Physical Journal B, 86, 258, 2013.

  4. J. Z. Yang, X. Wu and X. Li, A generalized Irving-Kirkwood formula for the calculation of stress in molecular dynamics models, Journal of Chemical Physics, 137, 134104 (2012).

  5. X. Li, An atomistic-based boundary element method for the reduction of the molecular Statics Models. Computer Methods in Applied Mechanics and Engineering .
    Vol 225, 1-13, 2012
  6. X. Li, A coarse-grained molecular dynamics model for crystalline solids, Int. J. Num. Meth. Eng. Vol 83, 986--997, 2010. [download preprint]

  7. X. Li, J.Z. Yang, and W. E, A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks, J. Comp. Phys. Vol 229, 3970-3987, 2010. [download preprint]

  8. X. Li, Efficient boundary condition for molecular statics models of solids Phys. Rev. B , Vol 80, 104112, 2009.

  9. X. Li, On the stability of boundary conditions for molecular dynamics. Journal of Computational and Applied Mathematics, Vol 231, 493-505, 2009.

  10. X. Li, Variational boundary condition for molecular dynamics: Treatment of the loading conditions. Journal of Computational Physics, Vol 227, 10078--10093, 2008.

  11. W. Wang, X. Li and C.W. Shu, The Discontinuous Galerkin Method for the Multiscale Modeling of Dynamics of Crystalline Solids. SIAM: Multiscale Modeling and Simulation, Vol 7, 294-320, 2008. .

  12. X. Li and W. E, Boundary conditions for molecular dynamics simulations of solids I: Treatment of the heat bath. Phys. Rev. B, vol 76, 104107, 2007.

  13. W. E, B. Engquist, X. Li, Weiqing Ren and E. Vanden-Eijnden, Heterogeneous multiscale methods: A review Commun. Comput. Phys. Vol 2, 367, 2007.

  14. J. Z. Yang and X. Li, Boundary conditions for molecular dynamics simulations of solids: a comparative study. Phys. Rev. B, vol 73, 224111, 2006. .

  15. X. Li and W. E, Boundary conditions for molecular dynamics simulations of solids at low temperature. Comm. Com. Phys., Vol 1, 136--176, 2006. PDF version .

  16. X. Li and W. E, Multiscale modeling of dynamics of solids at finite temperature .
    J. Mech. Phys. solids, Vol 53, 1650-1685, 2005..

  1. Error estimate for a multiscale method in Gas Dynamics
    (with Weinan E), method of analysis and application, Vol 11, 557--572, 2005..

  2. Multiscale modeling for crystalline solids.
    (with Weinan E), Handbook of multiscale material modeling (edited by Sidney Yip), 1491--1596, 2004.

  3. Some recent progress on multiscale modeling.
    (with Weinan E and Eric Vanden-Eijnden), lecture notes in Computational Science and Engineering, Vol. 3, 3--22, 2004..

  1. An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations
    (with John G. Wohlbier, Shi Jin and John Booske), Phys. Rev. E 70, 016502, 2004.

  2. On Two Moment Systems for computing multiphase semiclassical limits of the Schroedinger Equation
    (with Shi Jin and Laurent Gosse), Math. Model Methods Appl. Sci., vol 3, No. 12, 1689-1723, 2003 .
  3. Multi-phase Computations for semiclassical limits of Schroedinger Equation and related problems: Whitham vs Wigner.
    (with Shi Jin), Physica D, 182, 46-85, 2003.

  4. Numerical solutions of Pressure-less Gas Equations
    (with Francois Bouchut and Shi Jin), SIAM J. Num. Anal. 41, 135-158, 2003

B. Reports, Book Chapters and Conference Proceedings:
  1. Introduction to molecular dynamics simulations.
    Lecture Notes Series, Multiscale Modeling and Analysis for Materials Simulation, Institute for Mathematical Sciences, National University of Singapore: Volume 22, 95-146, 2011.

  2. Coarse-graining molecular dynamics.
    Mathematisches Forschungsinstitut Oberwolfach, Report 21, 2008, page 1148.

  3. Interface conditions for coupled atomistic and continuum models of solids for dynamics problems at finite temperature
    Material Research Society Proceedings, Paper no. 0978-GG06-02, 2006.