Jianfeng Lu | Scholars@Duke

Jianfeng Lu
Professor of Mathematics

Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.

More specifically, his current research focuses include:
Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.

Current Appointments & Affiliations

Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020
Associate Professor of Chemistry, Chemistry, Trinity College of Arts & Sciences 2016
Professor of Physics, Physics, Trinity College of Arts & Sciences 2020

Contact Information

242 Physics Bldg, 120 Science Drive, Durham, NC 27708
Mathematics Department, Duke University, Box 90320, Durham, NC 27708
jianfeng@math.duke.edu (919) 660-2875
Personal website

Background
Education, Training, & Certifications
- Ph.D., Princeton University 2009
Duke Appointment History
- Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016 - 2020
- Associate Professor in Physics, Physics, Trinity College of Arts & Sciences 2019 - 2020
- Associate Professor of Physics, Physics, Trinity College of Arts & Sciences 2016 - 2019
- Assistant Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2012 - 2016
- Assistant Professor in the Department of Physics, Physics, Trinity College of Arts & Sciences 2013 - 2016
- Assistant Professor in the Department of Chemistry, Chemistry, Trinity College of Arts & Sciences 2013 - 2016
Leadership & Clinical Positions at Duke
- Distinguished Lectures and Department Colloquium, August 2019
Recognition
In the News
- JUL 10, 2015
  
  Pratt Researchers to Harness Computational Power to Solve Time-Intensive Calculations
- FEB 15, 2013
  
  Sloan Foundation Names Charbonneau, Lu as 2013 Research Fellows
Awards & Honors
Expertise
Global Scholarship
- Teaching
  - China (Country)
Research
Selected Grants
- NRT-HDR: Harnessing AI for Autonomous Material Design awarded by National Science Foundation 2020 - 2025
- Innovation of Numerical Methods for High-Dimensional Problems awarded by National Science Foundation 2020 - 2023
- FET: Small: Efficient Inference Tools for Quantum Systems: Algorithms, Applications, and Analysis awarded by National Science Foundation 2019 - 2022
- HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by National Science Foundation 2019 - 2022
- EAGER-QAC-QSA: Resource Reduction in Quantum Computational Chemistry Mapping by Optimizing Orbital Basis Sets awarded by National Science Foundation 2020 - 2022
- Quantum Computing in Chemical and Material Sciences awarded by Department of Energy 2018 - 2021
- Collaborative Research: SI2-SSI: ELSI-Infrastructure for Scalable Electronic Structure Theory awarded by National Science Foundation 2015 - 2021
- CAREER: Research and training in advanced computational methods for quantum and statistical mechanics awarded by National Science Foundation 2015 - 2020
- Mathematical Problems for Electronic Structure Models awarded by National Science Foundation 2013 - 2016
Publications & Artistic Works
Selected Publications
- Academic Articles
  - Han, J., J. Lu, and M. Zhou. “Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach.” Journal of Computational Physics 423 (December 15, 2020). https://doi.org/10.1016/j.jcp.2020.109792.
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  - Lu, J., Y. Lu, and Z. Zhou. “Continuum limit and preconditioned Langevin sampling of the path integral molecular dynamics.” Journal of Computational Physics 423 (December 15, 2020). https://doi.org/10.1016/j.jcp.2020.109788.
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  - Sen, Deborshee, Matthias Sachs, Jianfeng Lu, and David B. Dunson. “Efficient posterior sampling for high-dimensional imbalanced logistic regression.” Biometrika 107, no. 4 (December 1, 2020): 1005–12. https://doi.org/10.1093/biomet/asaa035.
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  - Cai, Z., J. Lu, and S. Yang. “Inchworm Monte Carlo Method for Open Quantum Systems.” Communications on Pure and Applied Mathematics 73, no. 11 (November 1, 2020): 2430–72. https://doi.org/10.1002/cpa.21888.
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  - Li, Y., X. Cheng, and J. Lu. “Butterfly-net: Optimal function representation based on convolutional neural networks.” Communications in Computational Physics 28, no. 5 (November 1, 2020): 1838–85. https://doi.org/10.4208/CICP.OA-2020-0214.
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  - Lu, J., and S. Steinerberger. “Synchronization of Kuramoto oscillators in dense networks.” Nonlinearity 33, no. 11 (November 1, 2020): 5905–18. https://doi.org/10.1088/1361-6544/ab9baa.
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  - Yu, V. W. Z., C. Campos, W. Dawson, A. García, V. Havu, B. Hourahine, W. P. Huhn, et al. “ELSI — An open infrastructure for electronic structure solvers.” Computer Physics Communications 256 (November 1, 2020). https://doi.org/10.1016/j.cpc.2020.107459.
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  - Li, Yingzhou, and Jianfeng Lu. “Optimal Orbital Selection for Full Configuration Interaction (OptOrbFCI): Pursuing the Basis Set Limit under a Budget.” Journal of Chemical Theory and Computation 16, no. 10 (October 2020): 6207–21. https://doi.org/10.1021/acs.jctc.0c00613.
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  - Li, W., J. Lu, and L. Wang. “Fisher information regularization schemes for Wasserstein gradient flows.” Journal of Computational Physics 416 (September 1, 2020). https://doi.org/10.1016/j.jcp.2020.109449.
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  - Gao, Y., J. G. Liu, J. Lu, and J. L. Marzuola. “Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects.” Nonlinearity 33, no. 8 (August 1, 2020): 3816–45. https://doi.org/10.1088/1361-6544/ab853d.
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  - Ge, R., H. Lee, and J. Lu. “Estimating normalizing constants for log-concave distributions: Algorithms and lower bounds.” Proceedings of the Annual Acm Symposium on Theory of Computing, June 8, 2020, 579–86. https://doi.org/10.1145/3357713.3384289.
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  - Nishimura, A., D. B. Dunson, and J. Lu. “Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods.” Biometrika 107, no. 2 (June 1, 2020): 365–80. https://doi.org/10.1093/biomet/asz083.
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  - Li, Y., J. Lu, and A. Mao. “Variational training of neural network approximations of solution maps for physical models.” Journal of Computational Physics 409 (May 15, 2020). https://doi.org/10.1016/j.jcp.2020.109338.
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  - Lu, J., M. Sachs, and S. Steinerberger. “Quadrature Points via Heat Kernel Repulsion.” Constructive Approximation 51, no. 1 (February 1, 2020): 27–48. https://doi.org/10.1007/s00365-019-09471-4.
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  - Agazzi, Andrea, and Jianfeng Lu. “Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime.” Corr abs/2010.11858 (2020).
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  - CHEN, Z., Y. LI, and J. LU. “Tensor ring decomposition: Optimization landscape and one-loop convergence of alternating least squares.” Siam Journal on Matrix Analysis and Applications 41, no. 3 (January 1, 2020): 1416–42. https://doi.org/10.1137/19M1270689.
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  - Chen, K., Q. Li, J. Lu, and S. J. Wright. “Randomized sampling for basis function construction in generalized finite element methods.” Multiscale Modeling and Simulation 18, no. 2 (January 1, 2020): 1153–77. https://doi.org/10.1137/18M1166432.
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  - Chen, K., Q. Li, J. Lu, and S. J. Wright. “Random sampling and efficient algorithms for multiscale pdes.” Siam Journal on Scientific Computing 42, no. 5 (January 1, 2020): A2974–3005. https://doi.org/10.1137/18M1207430.
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  - Cheng, Cheng, Ingrid Daubechies, Nadav Dym, and Jianfeng Lu. “Stable Phase Retrieval from Locally Stable and Conditionally Connected Measurements. (null)” Corr abs/2006.11709 (2020).
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  - Khoo, Y., J. Lu, and L. Ying. “Solving parametric PDE problems with artificial neural networks.” European Journal of Applied Mathematics, January 1, 2020. https://doi.org/10.1017/S0956792520000182.
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  - Li, L., Y. Li, J. G. Liu, Z. Liu, and J. Lu. “A stochastic version of stein variational gradient descent for efficient sampling.” Communications in Applied Mathematics and Computational Science 15, no. 1 (January 1, 2020): 37–63. https://doi.org/10.2140/camcos.2020.15.37.
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  - Lu, J., A. B. Watson, and M. I. Weinstein. “Dirac operators and domain walls.” Siam Journal on Mathematical Analysis 52, no. 2 (January 1, 2020): 1115–45. https://doi.org/10.1137/19M127416X.
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  - Lu, J., and S. Steinerberger. “A dimension-free hermite-hadamard inequality via gradient estimates for the torsion function.” Proceedings of the American Mathematical Society 148, no. 2 (January 1, 2020): 673–79. https://doi.org/10.1090/proc/14843.
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  - Lu, J., and S. Steinerberger. “Optimal Trapping for Brownian Motion: a Nonlinear Analogue of the Torsion Function.” Potential Analysis, January 1, 2020. https://doi.org/10.1007/s11118-020-09845-5.
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  - Lu, J., and Z. Wang. “The full configuration interaction quantum monte carlo method through the lens of inexact power iteration.” Siam Journal on Scientific Computing 42, no. 1 (January 1, 2020): B1–29. https://doi.org/10.1137/18M1166626.
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  - Chen, H., Q. Li, and J. Lu. “A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer.” Journal of Computational Physics 398 (December 1, 2019). https://doi.org/10.1016/j.jcp.2019.108893.
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  - Lu, J., C. D. Sogge, and S. Steinerberger. “Approximating pointwise products of Laplacian eigenfunctions.” Journal of Functional Analysis 277, no. 9 (November 1, 2019): 3271–82. https://doi.org/10.1016/j.jfa.2019.05.025.
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  - Cao, Y., J. Lu, and Y. Lu. “Exponential Decay of Rényi Divergence Under Fokker–Planck Equations.” Journal of Statistical Physics 176, no. 5 (September 1, 2019): 1172–84. https://doi.org/10.1007/s10955-019-02339-8.
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  - Liu, J. G., J. Lu, D. Margetis, and J. L. Marzuola. “Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model.” Physica D: Nonlinear Phenomena 393 (June 1, 2019): 54–67. https://doi.org/10.1016/j.physd.2019.01.004.
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  - Wang, Zhe, Yingzhou Li, and Jianfeng Lu. “Coordinate Descent Full Configuration Interaction.” Journal of Chemical Theory and Computation 15, no. 6 (June 2019): 3558–69. https://doi.org/10.1021/acs.jctc.9b00138.
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  - Cao, Y., J. Lu, and Y. Lu. “Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance.” Journal of Mathematical Physics 60, no. 5 (May 1, 2019). https://doi.org/10.1063/1.5083065.
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  - Lin, L., J. Lu, and L. Ying. “Numerical methods for Kohn-Sham density functional theory.” Acta Numerica 28 (May 1, 2019): 405–539. https://doi.org/10.1017/S0962492919000047.
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  - Lu, J., and E. Vanden-Eijnden. “Methodological and Computational Aspects of Parallel Tempering Methods in the Infinite Swapping Limit.” Journal of Statistical Physics 174, no. 3 (February 15, 2019): 715–33. https://doi.org/10.1007/s10955-018-2210-y.
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  - Li, Yingzhou, and Jianfeng Lu. “Bold diagrammatic Monte Carlo in the lens of stochastic iterative methods.” Transactions of Mathematics and Its Applications 3, no. 1 (February 1, 2019). https://doi.org/10.1093/imatrm/tnz001.
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  - Martinsson, A., J. Lu, B. Leimkuhler, and E. Vanden-Eijnden. “The simulated tempering method in the infinite switch limit with adaptive weight learning.” Journal of Statistical Mechanics: Theory and Experiment 2019, no. 1 (January 16, 2019). https://doi.org/10.1088/1742-5468/aaf323.
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  - Agazzi, Andrea, and Jianfeng Lu. “Temporal-difference learning for nonlinear value function approximation in the lazy training regime.” Corr abs/1905.10917 (2019).
  - Cao, Y., and J. Lu. “Tensorization of the strong data processing inequality for quantum chi-square divergences.” Quantum 3 (January 1, 2019). https://doi.org/10.22331/q-2019-10-28-199.
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  - Gauckler, L., J. Lu, J. L. Marzuola, F. Rousset, and K. Schratz. “Trigonometric integrators for quasilinear wave equations.” Mathematics of Computation 88, no. 316 (January 1, 2019): 717–49. https://doi.org/10.1090/mcom/3339.
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  - Huang, H., J. G. Liu, and J. Lu. “Learning interacting particle systems: Diffusion parameter estimation for aggregation equations.” Mathematical Models and Methods in Applied Sciences 29, no. 1 (January 1, 2019): 1–29. https://doi.org/10.1142/S0218202519500015.
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  - Lu, J., Y. Lu, and J. Nolen. “Scaling limit of the Stein variational gradient descent: The mean field regime.” Siam Journal on Mathematical Analysis 51, no. 2 (January 1, 2019): 648–71. https://doi.org/10.1137/18M1187611.
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  - Yingzhou, L. I., L. U. Jianfeng, and A. Z. H. E. Wang. “Coordinatewise descent methods for leading eigenvalue problem.” Siam Journal on Scientific Computing 41, no. 4 (January 1, 2019): A2681–2716. https://doi.org/10.1137/18M1202505.
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  - Zhu, Wei, Qiang Qiu, Bao Wang, Jianfeng Lu, Guillermo Sapiro, and Ingrid Daubechies. “Stop Memorizing: A Data-Dependent Regularization Framework for Intrinsic Pattern Learning.” Siam J. Math. Data Sci. 1 (2019): 476–96.
  - Cao, Y., and J. Lu. “Stochastic dynamical low-rank approximation method.” Journal of Computational Physics 372 (November 1, 2018): 564–86. https://doi.org/10.1016/j.jcp.2018.06.058.
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  - Chen, H., J. Lu, and C. Ortner. “Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding.” Archive for Rational Mechanics and Analysis 230, no. 2 (November 1, 2018): 701–33. https://doi.org/10.1007/s00205-018-1256-y.
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  - Li, X., J. Liu, J. Lu, and X. Zhou. “Moderate deviation for random elliptic PDE with small noise.” Annals of Applied Probability 28, no. 5 (October 1, 2018): 2781–2813. https://doi.org/10.1214/17-AAP1373.
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  - Lu, J., and S. Steinerberger. “Detecting localized eigenstates of linear operators.” Research in Mathematical Sciences 5, no. 3 (September 1, 2018). https://doi.org/10.1007/s40687-018-0152-2.
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  - Barthel, T., and J. Lu. “Fundamental Limitations for Measurements in Quantum Many-Body Systems.” Physical Review Letters 121, no. 8 (August 24, 2018). https://doi.org/10.1103/PhysRevLett.121.080406.
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  - Huang, Y., J. Lu, and P. Ming. “A Concurrent Global–Local Numerical Method for Multiscale PDEs.” Journal of Scientific Computing 76, no. 2 (August 1, 2018): 1188–1215. https://doi.org/10.1007/s10915-018-0662-5.
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  - You, Zhiyi, Liying Li, Jianfeng Lu, and Hao Ge. “Integrated tempering enhanced sampling method as the infinite switching limit of simulated tempering.” The Journal of Chemical Physics 149, no. 8 (August 2018): 084114. https://doi.org/10.1063/1.5045369.
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  - Lin, L., J. Lu, and E. Vanden-Eijnden. “A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning).” Communications on Pure and Applied Mathematics 71, no. 6 (June 1, 2018): 1149–77. https://doi.org/10.1002/cpa.21725.
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  - Lu, Jianfeng, and Zhennan Zhou. “Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping.” The Journal of Chemical Physics 148, no. 6 (February 2018): 064110. https://doi.org/10.1063/1.5005024.
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  - Cai, Z., and J. Lu. “A surface hopping Gaussian beam method for high-dimensional transport systems.” Siam Journal on Scientific Computing 40, no. 5 (January 1, 2018): B1277–1301. https://doi.org/10.1137/17M1121299.
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  - Cai, Z., and J. Lu. “A quantum kinetic monte carlo method for quantum many-body spin dynamics.” Siam Journal on Scientific Computing 40, no. 3 (January 1, 2018): B706–22. https://doi.org/10.1137/17M1145446.
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  - Dai, S., B. Li, and J. Lu. “Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation.” Archive for Rational Mechanics and Analysis 227, no. 1 (January 1, 2018): 105–47. https://doi.org/10.1007/s00205-017-1158-4.
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  - Delgadillo, R., J. Lu, and X. Yang. “Frozen Gaussian approximation for high frequency wave propagation in periodic media.” Asymptotic Analysis 110, no. 3–4 (January 1, 2018): 113–35. https://doi.org/10.3233/ASY-181479.
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  - Du, Q., X. H. Li, J. Lu, and X. Tian. “A quasi-nonlocal coupling method for nonlocal and local diffusion models.” Siam Journal on Numerical Analysis 56, no. 3 (January 1, 2018): 1386–1404. https://doi.org/10.1137/17M1124012.
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  - Fang, D., and J. Lu. “A diabatic surface hopping algorithm based on time dependent perturbation theory and semiclassical analysis.” Multiscale Modeling and Simulation 16, no. 4 (January 1, 2018): 1603–22. https://doi.org/10.1137/17M1138042.
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  - Lai, R., and J. Lu. “Point cloud discretization of Fokker-planck operators for committor functions.” Multiscale Modeling and Simulation 16, no. 2 (January 1, 2018): 710–26. https://doi.org/10.1137/17M1123018.
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  - Lu, J., and H. Yang. “Phase-space sketching for crystal image analysis based on synchrosqueezed transforms.” Siam Journal on Imaging Sciences 11, no. 3 (January 1, 2018): 1954–78. https://doi.org/10.1137/17M1129441.
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  - Lu, J., and K. Spiliopoulos. “Analysis of multiscale integrators for multiple attractors and irreversible langevin samplers.” Multiscale Modeling and Simulation 16, no. 4 (January 1, 2018): 1859–83. https://doi.org/10.1137/16M1083748.
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  - Lu, J., and Z. Zhou. “Frozen gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms.” Mathematics of Computation 87, no. 313 (January 1, 2018): 2189–2232. https://doi.org/10.1090/mcom/3310.
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  - Yu, V. W. Z., F. Corsetti, A. García, W. P. Huhn, M. Jacquelin, W. Jia, B. Lange, et al. “ELSI: A unified software interface for Kohn–Sham electronic structure solvers.” Computer Physics Communications 222 (January 1, 2018): 267–85. https://doi.org/10.1016/j.cpc.2017.09.007.
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  - Zhu, Wei, Qiang Qiu, Bao Wang, Jianfeng Lu, Guillermo Sapiro, and Ingrid Daubechies. “Stop memorizing: A data-dependent regularization framework for intrinsic pattern learning.” Corr abs/1805.07291 (2018).
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  - Lu, J., and K. Thicke. “Cubic scaling algorithms for RPA correlation using interpolative separable density fitting.” Journal of Computational Physics 351 (December 15, 2017): 187–202. https://doi.org/10.1016/j.jcp.2017.09.012.
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  - Cao, Y., and J. Lu. “Lindblad equation and its semiclassical limit of the Anderson-Holstein model.” Journal of Mathematical Physics 58, no. 12 (December 1, 2017). https://doi.org/10.1063/1.4993431.
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  - Li, L., J. G. Liu, and J. Lu. “Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem.” Journal of Statistical Physics 169, no. 2 (October 1, 2017): 316–39. https://doi.org/10.1007/s10955-017-1866-z.
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  - Li, Q., J. Lu, and W. Sun. “A convergent method for linear half-space kinetic equations.” Esaim: Mathematical Modelling and Numerical Analysis 51, no. 5 (September 1, 2017): 1583–1615. https://doi.org/10.1051/m2an/2016076.
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  - Lu, Jianfeng, and Stefan Steinerberger. “A variation on the Donsker-Varadhan inequality for the principal eigenvalue.” Proceedings. Mathematical, Physical, and Engineering Sciences 473, no. 2204 (August 23, 2017): 20160877. https://doi.org/10.1098/rspa.2016.0877.
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  - Lu, J., and H. Yang. “A cubic scaling algorithm for excited states calculations in particle–particle random phase approximation.” Journal of Computational Physics 340 (July 1, 2017): 297–308. https://doi.org/10.1016/j.jcp.2017.03.055.
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  - Gao, Y., J. G. Liu, and J. Lu. “Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces.” Journal of Nonlinear Science 27, no. 3 (June 1, 2017): 873–926. https://doi.org/10.1007/s00332-016-9354-1.
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  - Li, Chen, Jianfeng Lu, and Weitao Yang. “On extending Kohn-Sham density functionals to systems with fractional number of electrons.” The Journal of Chemical Physics 146, no. 21 (June 2017): 214109. https://doi.org/10.1063/1.4982951.
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  - Lu, J., and K. Thicke. “Orbital minimization method with ℓ¹ regularization.” Journal of Computational Physics 336 (May 1, 2017): 87–103. https://doi.org/10.1016/j.jcp.2017.02.005.
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  - Huang, Y., Jianfeng Lu, and P. Ming. “A Hybrid Global-local Numerical Method for Multiscale PDEs,” April 23, 2017.
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  - Li, L., J. -. G. Liu, and Jianfeng Lu. “Fractional stochastic differential equations satisfying fluctuation-dissipation theorem,” April 23, 2017.
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  - Lu, Jianfeng, and Zhennan Zhou. “Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems.” The Journal of Chemical Physics 146, no. 15 (April 2017): 154110. https://doi.org/10.1063/1.4981021.
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  - Niu, X., T. Luo, J. Lu, and Y. Xiang. “Dislocation climb models from atomistic scheme to dislocation dynamics.” Journal of the Mechanics and Physics of Solids 99 (February 1, 2017): 242–58. https://doi.org/10.1016/j.jmps.2016.11.012.
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  - Watson, A. B., J. Lu, and M. I. Weinstein. “Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature.” Journal of Mathematical Physics 58, no. 2 (February 1, 2017). https://doi.org/10.1063/1.4976200.
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  - Cornelis, Bruno, Haizhao Yang, Alex Goodfriend, Noelle Ocon, Jianfeng Lu, and Ingrid Daubechies. “Removal of Canvas Patterns in Digital Acquisitions of Paintings.” Ieee Transactions on Image Processing : A Publication of the Ieee Signal Processing Society 26, no. 1 (January 2017): 160–71. https://doi.org/10.1109/tip.2016.2621413.
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  - Gao, Y., J. G. Liu, and J. Lu. “Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime.” Siam Journal on Mathematical Analysis 49, no. 3 (January 1, 2017): 1705–31. https://doi.org/10.1137/16M1094543.
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  - Li, Q., J. Lu, and W. Sun. “Validity and Regularization of Classical Half-Space Equations.” Journal of Statistical Physics 166, no. 2 (January 1, 2017): 398–433. https://doi.org/10.1007/s10955-016-1688-4.
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  - Li, Q., J. Lu, and W. Sun. “Half-space kinetic equations with general boundary conditions.” Mathematics of Computation 86, no. 305 (January 1, 2017): 1269–1301. https://doi.org/10.1090/mcom/3155.
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  - Li, Q., and J. Lu. “An asymptotic preserving method for transport equations with oscillatory scattering coefficients.” Multiscale Modeling and Simulation 15, no. 4 (January 1, 2017): 1694–1718. https://doi.org/10.1137/16M109212X.
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  - Li, X. H., and J. Lu. “Quasi-nonlocal coupling of nonlocal diffusions.” Siam Journal on Numerical Analysis 55, no. 5 (January 1, 2017): 2394–2415. https://doi.org/10.1137/16M1086443.
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  - Lu, J., and H. Yang. “Preconditioning orbital minimization method for planewave discretization.” Multiscale Modeling and Simulation 15, no. 1 (January 1, 2017): 254–73. https://doi.org/10.1137/16M1068670.
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  - Mendl, Christian B., Jianfeng Lu, and Jani Lukkarinen. “Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory.” Physical Review. E 94, no. 6–1 (December 2, 2016): 062104. https://doi.org/10.1103/physreve.94.062104.
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  - Yu, Tang-Qing, Jianfeng Lu, Cameron F. Abrams, and Eric Vanden-Eijnden. “Multiscale implementation of infinite-swap replica exchange molecular dynamics.” Proceedings of the National Academy of Sciences of the United States of America 113, no. 42 (October 3, 2016): 11744–49. https://doi.org/10.1073/pnas.1605089113.
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  - Lu, Jianfeng, and Zhennan Zhou. “Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics.” The Journal of Chemical Physics 145, no. 12 (September 2016): 124109. https://doi.org/10.1063/1.4963107.
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  - Li, X., and J. Lu. “Traction boundary conditions for molecular static simulations.” Computer Methods in Applied Mechanics and Engineering 308 (August 15, 2016): 310–29. https://doi.org/10.1016/j.cma.2016.05.002.
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  - Lin, L., and J. Lu. “Decay estimates of discretized Green’s functions for Schrödinger type operators.” Science China Mathematics 59, no. 8 (August 1, 2016): 1561–78. https://doi.org/10.1007/s11425-016-0311-4.
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  - Lai, R., and J. Lu. “Localized density matrix minimization and linear-scaling algorithms.” Journal of Computational Physics 315 (June 15, 2016): 194–210. https://doi.org/10.1016/j.jcp.2016.02.076.
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  - Lu, J., and L. Ying. “Sparsifying preconditioner for soliton calculations.” Journal of Computational Physics 315 (June 15, 2016): 458–66. https://doi.org/10.1016/j.jcp.2016.03.061.
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  - Lu, J., B. Wirth, and H. Yang. “Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis.” Journal of the Mechanics and Physics of Solids 89 (April 1, 2016): 194–210. https://doi.org/10.1016/j.jmps.2016.01.002.
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  - Chen, J., and J. Lu. “Analysis 0f the divide-and-conquer method for electronic structure calculations.” Mathematics of Computation 85, no. 302 (January 1, 2016): 2919–38. https://doi.org/10.1090/mcom/3066.
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  - Delgadillo, R., J. Lu, and X. Yang. “Gauge-invariant frozen Gaussian approximation method for the schrödinger equation with periodic potentials.” Siam Journal on Scientific Computing 38, no. 4 (January 1, 2016): A2440–63. https://doi.org/10.1137/15M1040384.
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  - Li, Chen, Jianfeng Lu, and Weitao Yang. “Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of Kohn-Sham density functionals.” The Journal of Chemical Physics 143, no. 22 (December 2015): 224110. https://doi.org/10.1063/1.4936411.
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  - Lu, J., V. Moroz, and C. B. Muratov. “Orbital-Free Density Functional Theory of Out-of-Plane Charge Screening in Graphene.” Journal of Nonlinear Science 25, no. 6 (December 1, 2015): 1391–1430. https://doi.org/10.1007/s00332-015-9259-4.
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  - Li, Q., J. Lu, and W. Sun. “Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics.” Journal of Computational Physics 292 (July 1, 2015): 141–67. https://doi.org/10.1016/j.jcp.2015.03.014.
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  - Yang, H., J. Lu, W. P. Brown, I. Daubechies, and L. Ying. “Quantitative canvas weave analysis using 2-D synchrosqueezed transforms: Application of time-frequency analysis to art investigation.” Ieee Signal Processing Magazine 32, no. 4 (July 1, 2015): 55–63. https://doi.org/10.1109/MSP.2015.2406882.
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  - Lu, J., and C. B. Mendl. “Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation.” Journal of Computational Physics 291 (June 5, 2015): 303–16. https://doi.org/10.1016/j.jcp.2015.03.020.
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  - Lu, J., J. G. Liu, and D. Margetis. “Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions.” Physical Review E Statistical, Nonlinear, and Soft Matter Physics 91, no. 3 (March 4, 2015). https://doi.org/10.1103/PhysRevE.91.032403.
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  - Lu, Jianfeng, and James Nolen. “Reactive trajectories and the transition path process.” Probability Theory and Related Fields 161, no. 1–2 (February 2015): 195–244. https://doi.org/10.1007/s00440-014-0547-y.
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  - Lai, R., J. Lu, and S. Osher. “Density matrix minimization with ℓ1 regularization.” Communications in Mathematical Sciences 13, no. 8 (January 1, 2015): 2097–2117. https://doi.org/10.4310/CMS.2015.v13.n8.a6.
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  - Liu, J., J. Lu, and X. Zhou. “Efficient rare event simulation for failure problems in random media.” Siam Journal on Scientific Computing 37, no. 2 (January 1, 2015): A609–24. https://doi.org/10.1137/140965569.
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  - Lu, J., and J. L. Marzuola. “Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics.” Communications in Mathematical Sciences 13, no. 5 (January 1, 2015): 1051–74. https://doi.org/10.4310/CMS.2015.v13.n5.a1.
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  - Lu, J., and L. Ying. “Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost.” Journal of Computational Physics 302 (2015): 329–35. https://doi.org/10.1016/j.jcp.2015.09.014.
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  - Yang, H., J. Lu, and L. Ying. “Crystal image analysis using 2D synchrosqueezed transforms.” Multiscale Modeling and Simulation 13, no. 4 (January 1, 2015): 1542–72. https://doi.org/10.1137/140955872.
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  - Lu, Jianfeng, and Felix Otto. “Nonexistence of a Minimizer for Thomas-Fermi-Dirac-von Weizsäcker Model.” Communications on Pure and Applied Mathematics 67, no. 10 (October 2014): 1605–17. https://doi.org/10.1002/cpa.21477.
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  - Yang, Yang, Degao Peng, Jianfeng Lu, and Weitao Yang. “Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies.” The Journal of Chemical Physics 141, no. 12 (September 28, 2014): 124104–124104. https://doi.org/10.1063/1.4895792.
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  - Lu, Jianfeng, and Eric Vanden-Eijnden. “Exact dynamical coarse-graining without time-scale separation.” The Journal of Chemical Physics 141, no. 4 (July 28, 2014): 044109–044109. https://doi.org/10.1063/1.4890367.
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  - E, W., and J. Lu. “Mathematical theory of solids: From quantum mechanics to continuum models.” Discrete and Continuous Dynamical Systems 34, no. 12 (June 2014): 5085–97. https://doi.org/10.3934/dcds.2014.34.5085.
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  - Kohn, R. V., J. Lu, B. Schweizer, and M. I. Weinstein. “A variational perspective on cloaking by anomalous localized resonance.” Communications in Mathematical Physics 328, no. 1 (March 14, 2014): 1–27. https://doi.org/10.1007/s00220-014-1943-y.
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  - Lin, L., J. Lu, and S. Shao. “Analysis of time reversible born-oppenheimer molecular dynamics.” Entropy 16, no. 1 (January 1, 2014): 110–37. https://doi.org/10.3390/e16010110.
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  - Lu, J., and P. Ming. “Stability of a force-based hybrid method with planar sharp interface.” Siam Journal on Numerical Analysis 52, no. 4 (January 1, 2014): 2005–26. https://doi.org/10.1137/130904843.
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  - Lu, Jian-feng, and Xu Yang. “Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase.” Acta Mathematicae Applicatae Sinica, English Series 29, no. 3 (July 2013): 465–76. https://doi.org/10.1007/s10255-011-0095-5.
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  - Lu, Jianfeng, and Eric Vanden-Eijnden. “Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials.” The Journal of Chemical Physics 138, no. 8 (February 2013): 084105. https://doi.org/10.1063/1.4790706.
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  - E, W., J. Lu, and Y. Yao. “The landscape of complex networks: Critical nodes and a hierarchical decomposition.” Methods and Applications of Analysis 20, no. 4 (2013): 383–404. https://doi.org/10.4310/MAA.2013.v20.n4.a5.
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  - Lu, Jianfeng, and Pingbing Ming. “Convergence of a Force-Based Hybrid Method in Three Dimensions.” Communications on Pure and Applied Mathematics 66, no. 1 (January 2013): 83–108. https://doi.org/10.1002/cpa.21429.
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  - E, Weinan, and Jianfeng Lu. “Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model.” Journal of Mathematical Physics 53, no. 11 (November 2012): 115615–115615. https://doi.org/10.1063/1.4755952.
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  - Lu, J., and X. Yang. “Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods.” Multiscale Modeling and Simulation 10, no. 2 (September 7, 2012): 451–72. https://doi.org/10.1137/10081068X.
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  - Lu, J., and X. Yang. “Convergence of frozen Gaussian approximation for high-frequency wave propagation.” Communications on Pure and Applied Mathematics 65, no. 6 (June 1, 2012): 759–89. https://doi.org/10.1002/cpa.21384.
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  - Lin, Lin, Jianfeng Lu, Lexing Ying, and Weinan E. “Optimized local basis set for Kohn–Sham density functional theory.” Journal of Computational Physics 231, no. 13 (May 2012): 4515–29. https://doi.org/10.1016/j.jcp.2012.03.009.
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  - Lin, Lin, Jianfeng Lu, Lexing Ying, and Weinan E. “Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation.” Journal of Computational Physics 231, no. 4 (February 2012): 2140–54. https://doi.org/10.1016/j.jcp.2011.11.032.
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  - E, Weinan, and Jianfeng Lu. “The Kohn-Sham equation for deformed crystals.” Memoirs of the American Mathematical Society 221, no. 1040 (2012): 1–1. https://doi.org/10.1090/s0065-9266-2012-00659-9.
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  - Daubechies, Ingrid, Jianfeng Lu, and Hau-Tieng Wu. “Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool.” Applied and Computational Harmonic Analysis 30, no. 2 (March 2011): 243–61. https://doi.org/10.1016/j.acha.2010.08.002.
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  - E, Weinan, and Jianfeng Lu. “The Electronic Structure of Smoothly Deformed Crystals: Wannier Functions and the Cauchy–Born Rule.” Archive for Rational Mechanics and Analysis 199, no. 2 (February 2011): 407–33. https://doi.org/10.1007/s00205-010-0339-1.
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  - Lin, Lin, Chao Yang, Juan C. Meza, Jianfeng Lu, Lexing Ying, and Weinan E. “SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix.” Acm Transactions on Mathematical Software 37, no. 4 (February 2011): 1–19. https://doi.org/10.1145/1916461.1916464.
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  - E, W., J. Lu, and X. Yang. “Effective Maxwell equations from time-dependent density functional theory.” Acta Math. Sin. 32 (2011): 339–339.
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  - Lin, L., J. Lu, and L. Ying. “Fast construction of hierarchical matrix representation from matrix-vector multiplication.” Journal of Computational Physics 230, no. 10 (January 1, 2011): 4071–87. https://doi.org/10.1016/j.jcp.2011.02.033.
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  - Lin, Lin, Chao Yang, Jianfeng Lu, Lexing Ying, and Weinan E. “A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations.” Siam Journal on Scientific Computing 33, no. 3 (January 2011): 1329–51. https://doi.org/10.1137/09077432x.
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  - Lu, J., and X. Yang. “Frozen Gaussian approximation for high frequency wave propagation.” Communications in Mathematical Sciences 9, no. 3 (2011): 663–83.
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  - Noe, Frank, Marco Sarich, Christof Schutte, and Eric Vanden-Eijnden. “Markov state models based on milestoning.” J. Chem. Phys. 134 (2011): 204105.
  - E, Weinan, and Jianfeng Lu. “Electronic structure of smoothly deformed crystals: Cauchy-born rule for the nonlinear tight-binding model.” Communications on Pure and Applied Mathematics 63, no. 11 (November 2010): 1432–68. https://doi.org/10.1002/cpa.20330.
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  - E, W., T. Li, and J. Lu. “Localized bases of eigensubspaces and operator compression.” Proceedings of the National Academy of Sciences 107, no. 4 (January 26, 2010): 1273–78. https://doi.org/10.1073/pnas.0913345107.
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  - Lin, Lin, Jianfeng Lu, Lexing Ying, Roberto Car, and Weinan E. “Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems.” Commun. Math. Sci. 7 (2009): 755–77.
  - Lin, Lin, Jianfeng Lu, Lexing Ying, and Weinan E. “Pole-based approximation of the Fermi-Dirac function.” Chin. Ann. Math. Ser. B 30 (2009): 729–42.
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  - Garcia-Cervera, Carlos J., Weiqing Ren, Jianfeng Lu, and Weinan E. “Sequential multiscale modelling using sparse representation.” Commun. Comput. Phys. 4 (2008): 1025–33.
  - E, Weinan, and Jianfeng Lu. “The Elastic Continuum Limit of the Tight Binding Model*.” Chinese Annals of Mathematics, Series B 28, no. 6 (December 2007): 665–76. https://doi.org/10.1007/s11401-006-0447-2.
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  - E, Weinan, Carlos J. García-Cervera, and Jianfeng Lu. “A sub-linear scaling algorithm for computing the electronic structure of materials.” Communications in Mathematical Sciences 5, no. 4 (2007): 999–1026. https://doi.org/10.4310/cms.2007.v5.n4.a14.
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  - E, Weinan, and Jianfeng Lu. “Seamless multiscale modeling via dynamics on fiber bundles.” Communications in Mathematical Sciences 5, no. 3 (2007): 649–63. https://doi.org/10.4310/cms.2007.v5.n3.a7.
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  - E, Weinan, and Jianfeng Lu. “The continuum limit and QM-continuum approximation of quantum mechanical models of solids.” Communications in Mathematical Sciences 5, no. 3 (2007): 679–96. https://doi.org/10.4310/cms.2007.v5.n3.a9.
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  - An, Dong, Sara Y. Cheng, Teresa Head-Gordon, Lin Lin, and Jianfeng Lu. “Convergence of Stochastic-extended Lagrangian molecular dynamics method for polarizable force field simulation,” n.d.
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  - Cai, Zhenning, Jianfeng Lu, and Kevin Stubbs. “On discrete Wigner transforms,” n.d.
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  - Cai, Zhenning, Jianfeng Lu, and Siyao Yang. “Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth,” n.d.
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  - Cao, Yu, Jianfeng Lu, and Lihan Wang. “On explicit $L^2$-convergence rate estimate for underdamped Langevin dynamics (null),” n.d.
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  - Cao, Yu, Jianfeng Lu, and Lihan Wang. “Complexity of randomized algorithms for underdamped Langevin dynamics (null),” n.d.
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  - Chen, Ke, Qin Li, Jianfeng Lu, and Stephen J. Wright. “A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient,” n.d.
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  - Chen, Shi, Qin Li, Jianfeng Lu, and Stephen J. Wright. “Manifold Learning and Nonlinear Homogenization,” n.d.
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  - Chen, Ziang, Yingzhou Li, and Jianfeng Lu. “On the global convergence of randomized coordinate gradient descent for non-convex optimization,” n.d.
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  - Craig, Katy, Jian-Guo Liu, Jianfeng Lu, Jeremy L. Marzuola, and Li Wang. “A Proximal-Gradient Algorithm for Crystal Surface Evolution,” n.d.
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  - Ding, Zhiyan, Qin Li, Jianfeng Lu, and Stephen J. Wright. “Random Coordinate Langevin Monte Carlo,” n.d.
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  - Ding, Zhiyan, Qin Li, Jianfeng Lu, and Stephen J. Wright. “Random Coordinate Underdamped Langevin Monte Carlo,” n.d.
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  - Ding, Zhiyan, Qin Li, and Jianfeng Lu. “Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds,” n.d.
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  - E, Weinan, Jianfeng Lu, and Jerry Z. Yang. “Uniform accuracy of the quasicontinuum method.” Physical Review B 74, no. 21 (n.d.). https://doi.org/10.1103/physrevb.74.214115.
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  - E, Weinan, and Jianfeng Lu. “Multiscale modeling.” Scholarpedia 6, no. 10 (n.d.): 11527–11527. https://doi.org/10.4249/scholarpedia.11527.
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  - Gao, Yuan, Anya E. Katsevich, Jian-Guo Liu, Jianfeng Lu, and Jeremy L. Marzuola. “Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates,” n.d.
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  - García-Cervera, C. J., Jianfeng Lu, Yulin Xuan, and Weinan E. “Linear-scaling subspace-iteration algorithm with optimally localized nonorthogonal wave functions for Kohn-Sham density functional theory.” Physical Review B 79, no. 11 (n.d.). https://doi.org/10.1103/physrevb.79.115110.
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  - Ge, Rong, Holden Lee, Jianfeng Lu, and Andrej Risteski. “Efficient sampling from the Bingham distribution (null),” n.d.
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  - Han, Jiequn, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, and Linfeng Zhang. “Universal approximation of symmetric and anti-symmetric functions,” n.d.
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  - Holst, Michael, Houdong Hu, Jianfeng Lu, Jeremy L. Marzuola, Duo Song, and John Weare. “Symmetry Breaking in Density Functional Theory due to Dirac Exchange for a Hydrogen Molecule,” n.d.
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  - Khoo, Yuehaw, Jianfeng Lu, and Lexing Ying. “Efficient construction of tensor ring representations from sampling,” n.d.
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  - Kovalsky, Shahar Z., Noam Aigerman, Ingrid Daubechies, Michael Kazhdan, Jianfeng Lu, and Stefan Steinerberger. “Non-Convex Planar Harmonic Maps,” n.d.
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  - Li, Lei, Jianfeng Lu, Jonathan Mattingly, and Lihan Wang. “Numerical methods for stochastic differential equations based on Gaussian mixture (null),” n.d.
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  - Li, Xiantao, Lin Lin, and Jianfeng Lu. “PEXSI-$Σ$: A Green's function embedding method for Kohn-Sham density functional theory,” n.d.
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  - Lin, Lin, Jianfeng Lu, Roberto Car, and Weinan E. “Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems.” Physical Review B 79, no. 11 (n.d.). https://doi.org/10.1103/physrevb.79.115133.
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  - Loring, Terry A., Jianfeng Lu, and Alexander B. Watson. “Locality of the windowed local density of states,” n.d.
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  - Lu, Jianfeng, Cody Murphey, and Stefan Steinerberger. “Fast localization of eigenfunctions via smoothed potentials,” n.d.
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  - Lu, Jianfeng, Jeremy L. Marzuola, and Alexander B. Watson. “Defect resonances of truncated crystal structures,” n.d.
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  - Lu, Jianfeng, Yulong Lu, and Min Wang. “A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations,” n.d.
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  - Lu, Jianfeng, Zihang Zhang, and Zhennan Zhou. “Bloch dynamics with second order Berry phase correction,” n.d.
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  - Lu, Jianfeng, Zuowei Shen, Haizhao Yang, and Shijun Zhang. “Deep Network Approximation for Smooth Functions,” n.d.
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  - Lu, Jianfeng, and Felix Otto. “An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus,” n.d.
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  - Lu, Jianfeng, and Felix Otto. “Optimal artificial boundary condition for random elliptic media,” n.d.
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  - Lu, Jianfeng, and Haizhao Yang. “Preconditioning Orbital Minimization Method for Planewave Discretization,” n.d.
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  - Lu, Jianfeng, and Kevin D. Stubbs. “Algebraic localization implies exponential localization in non-periodic insulators,” n.d.
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  - Lu, Jianfeng, and Lexing Ying. “Fast algorithm for periodic density fitting for Bloch waves,” n.d.
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  - Lu, Jianfeng, and Lihan Wang. “On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes (null),” n.d.
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  - Lu, Jianfeng, and Lihan Wang. “Complexity of zigzag sampling algorithm for strongly log-concave distributions,” n.d.
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  - Lu, Jianfeng, and Stefan Steinerberger. “Riesz Energy on the Torus: Regularity of Minimizers,” n.d.
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  - Lu, Jianfeng, and Stefan Steinerberger. “On Pointwise Products of Elliptic Eigenfunctions,” n.d.
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  - Lu, Jianfeng, and Stefan Steinerberger. “Neural Collapse with Cross-Entropy Loss,” n.d.
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  - Lu, Yiping, Chao Ma, Yulong Lu, Jianfeng Lu, and Lexing Ying. “A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth,” n.d.
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  - Lu, Yulong, Jianfeng Lu, and James Nolen. “Accelerating Langevin Sampling with Birth-death,” n.d.
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  - Lu, Yulong, and Jianfeng Lu. “A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributions,” n.d.
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  - Nolen, J. H., Jianfeng Lu, and Yulong Lu. “Scaling limit of the Stein variational gradient descent: the mean field regime (Accepted).” Siam Journal on Mathematical Analysis, n.d.
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  - Sachs, Matthias, Deborshee Sen, Jianfeng Lu, and David Dunson. “Posterior computation with the Gibbs zig-zag sampler,” n.d.
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  - Stubbs, Kevin D., Alexander B. Watson, and Jianfeng Lu. “Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher,” n.d.
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  - Stubbs, Kevin D., Alexander B. Watson, and Jianfeng Lu. “The Iterated Projected Position Algorithm for Constructing Exponentially Localized Generalized Wannier Functions for Periodic and Non-Periodic Insulators in Two Dimensions and Higher,” n.d.
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  - Thicke, Kyle, Alexander B. Watson, and Jianfeng Lu. “Computing edge states without hard truncation,” n.d.
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- Conference Papers
  - Yu, Victor, William Dawson, Alberto Garcia, Ville Havu, Ben Hourahine, William Huhn, Mathias Jacquelin, et al. “Large-scale benchmark of electronic structure solvers with the ELSI infrastructure.” In Abstracts of Papers of the American Chemical Society, Vol. 257. AMER CHEMICAL SOC, 2019.
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  - Yu, Victor, William Huhn, Lin Lin, Jianfeng Lu, Alvaro Vazquez-Mayagoitia, Chao Yang, and Volker Blum. “ELSI: A unified software interface for Kohn-Sham electronic structure solvers.” In Abstracts of Papers of the American Chemical Society, Vol. 255. AMER CHEMICAL SOC, 2018.
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  - Xian, Y., A. Thompson, Q. Qiu, L. Nolte, D. Nowacek, J. Lu, and R. Calderbank. “Classification of whale vocalizations using the Weyl transform.” In Icassp, Ieee International Conference on Acoustics, Speech and Signal Processing Proceedings, 2015-August:773–77, 2015. https://doi.org/10.1109/ICASSP.2015.7178074.
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  - Xian, Yin, Andrew Thompson, Qiang Qiu, Loren Nolte, Douglas Nowacek, Jianfeng Lu, Robert Calderbank, and Robert IEEE. “CLASSIFICATION OF WHALE VOCALIZATIONS USING THE WEYL TRANSFORM.” In 2015 Ieee International Conference on Acoustics, Speech, and Signal Processing (Icassp), 773–77, 2015.
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  - Yang, X., and J. Lu. “Seismic modeling using the frozen Gaussian approximation.” In Society of Exploration Geophysicists International Exposition and 83rd Annual Meeting, Seg 2013: Expanding Geophysical Frontiers, 4677–82, 2013. https://doi.org/10.1190/segam2013-1225.1.
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