Jianfeng Lu
Associate 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.
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
 Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016
 Associate Professor of Chemistry, Chemistry, Trinity College of Arts & Sciences 2016
 Associate Professor of Physics, Physics, Trinity College of Arts & Sciences 2016
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) 6602875
 Personal website
 Background

Education, Training, & Certifications
 Ph.D., Princeton University 2009

Duke Appointment History
 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
 Recognition

In the News

Awards & Honors
 Expertise

Global Scholarship

Teaching

 Research

Selected Grants
 Quantum Computing in Chemical and Material Sciences awarded by Department of Energy 2018  2021
 CAREER: Research and training in advanced computational methods for quantum and statistical mechanics awarded by National Science Foundation 2015  2020
 Collaborative Research: SI2SSI: ELSIInfrastructure for Scalable Electronic Structure Theory 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
 Liu, JG, Lu, J, Margetis, D, and Marzuola, JL. "Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model(Accepted)." Physica D: Nonlinear Phenomena 393 (June 1, 2019): 5467. Full Text Open Access Copy
 Wang, Z, Li, Y, and Lu, J. "Coordinate Descent Full Configuration Interaction." Journal of Chemical Theory and Computation (May 10, 2019). Full Text
 Lu, J, and VandenEijnden, E. "Methodological and Computational Aspects of Parallel Tempering Methods in the Infinite Swapping Limit." Journal of Statistical Physics 174, no. 3 (February 15, 2019): 715733. Full Text Open Access Copy
 Li, Y, and Lu, J. "Bold diagrammatic Monte Carlo in the lens of stochastic iterative methods." Transactions of Mathematics and Its Applications 3, no. 1 (February 1, 2019): 117. Full Text Open Access Copy
 Martinsson, A, Lu, J, Leimkuhler, B, and VandenEijnden, E. "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). Full Text
 Gauckler, L, Lu, J, Marzuola, JL, Rousset, F, and Schratz, K. "Trigonometric integrators for quasilinear wave equations." Mathematics of Computation 88, no. 316 (January 1, 2019): 717749. Full Text
 Huang, H, Liu, JG, and Lu, J. "Learning interacting particle systems: Diffusion parameter estimation for aggregation equations." Mathematical Models and Methods in Applied Sciences 29, no. 1 (January 1, 2019): 129. Full Text Open Access Copy
 Lu, J, Lu, Y, and Nolen, J. "Scaling Limit of the Stein Variational Gradient Descent: The Mean Field Regime." Siam Journal on Mathematical Analysis 51, no. 2 (January 2019): 648671. Full Text
 Delgadillo, R, Lu, J, and Yang, X. "Frozen Gaussian approximation for high frequency wave propagation in periodic media." Asymptotic Analysis 110, no. 34 (November 19, 2018): 113135. Full Text
 Cao, Y, and Lu, J. "Stochastic dynamical lowrank approximation method." Journal of Computational Physics 372 (November 1, 2018): 564586. Full Text
 Chen, H, Lu, J, and Ortner, C. "Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding." Archive for Rational Mechanics and Analysis 230, no. 2 (November 1, 2018): 701733. Full Text Open Access Copy
 Li, X, Liu, J, Lu, J, and Zhou, X. "Moderate deviation for random elliptic PDE with small noise." Annals of Applied Probability 28, no. 5 (October 1, 2018): 27812813. Full Text Open Access Copy
 Barthel, T, and Lu, J. "Fundamental Limitations for Measurements in Quantum ManyBody Systems." Physical Review Letters 121, no. 8 (August 24, 2018). Full Text
 Huang, Y, Lu, J, and Ming, P. "A Concurrent Global–Local Numerical Method for Multiscale PDEs." Journal of Scientific Computing 76, no. 2 (August 1, 2018): 11881215. Full Text
 You, Z, Li, L, Lu, J, and Ge, H. "Integrated tempering enhanced sampling method as the infinite switching limit of simulated tempering." The Journal of Chemical Physics 149, no. 8 (August 2018): 084114null. Full Text
 Lin, L, Lu, J, and VandenEijnden, E. "A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)." Communications on Pure and Applied Mathematics 71, no. 6 (June 1, 2018): 11491177. Full Text Open Access Copy
 Lu, J, and Zhou, Z. "Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping." The Journal of Chemical Physics 148, no. 6 (February 2018): 064110null. Full Text Open Access Copy
 Cai, Z, and Lu, J. "A surface hopping Gaussian beam method for highdimensional transport systems." Siam Journal on Scientific Computing 40, no. 5 (January 1, 2018): B1277B1301. Full Text Open Access Copy
 Cai, Z, and Lu, J. "A quantum kinetic monte carlo method for quantum manybody spin dynamics." Siam Journal on Scientific Computing 40, no. 3 (January 1, 2018): B706B722. Full Text Open Access Copy
 Dai, S, Li, B, and Lu, J. "Convergence of PhaseField Free Energy and Boundary Force for Molecular Solvation." Archive for Rational Mechanics and Analysis 227, no. 1 (January 1, 2018): 105147. Full Text Open Access Copy
 Du, Q, Li, XH, Lu, J, and Tian, X. "A quasinonlocal coupling method for nonlocal and local diffusion models." Siam Journal on Numerical Analysis 56, no. 3 (January 1, 2018): 13861404. Full Text Open Access Copy
 Fang, D, and Lu, J. "A Diabatic Surface Hopping Algorithm Based on Time Dependent Perturbation Theory and Semiclassical Analysis." Multiscale Modeling & Simulation 16, no. 4 (January 2018): 16031622. Full Text Open Access Copy
 Lai, R, and Lu, J. "Point cloud discretization of Fokkerplanck operators for committor functions." Multiscale Modeling and Simulation 16, no. 2 (January 1, 2018): 710726. Full Text Open Access Copy
 Lu, J, and Spiliopoulos, K. "Analysis of multiscale integrators for multiple attractors and irreversible langevin samplers." Multiscale Modeling and Simulation 16, no. 4 (January 1, 2018): 18591883. Full Text
 Lu, J, and Yang, H. "Phasespace sketching for crystal image analysis based on synchrosqueezed transforms." Siam Journal on Imaging Sciences 11, no. 3 (January 1, 2018): 19541978. Full Text Open Access Copy
 Lu, J, and Zhou, Z. "Frozen gaussian approximation with surface hopping for mixed quantumclassical dynamics: A mathematical justification of fewest switches surface hopping algorithms." Mathematics of Computation 87, no. 313 (January 1, 2018): 21892232. Full Text Open Access Copy
 Yu, VWZ, Corsetti, F, García, A, Huhn, WP, Jacquelin, M, Jia, W, Lange, B, Lin, L, Lu, J, Mi, W, Seifitokaldani, A, VázquezMayagoitia, Á, Yang, C, Yang, H, and Blum, V. "ELSI: A unified software interface for Kohn–Sham electronic structure solvers." Computer Physics Communications 222 (January 1, 2018): 267285. Full Text Open Access Copy
 Zhu, W, Qiu, Q, Wang, B, Lu, J, Sapiro, G, and Daubechies, I. "Stop memorizing: A datadependent regularization framework for intrinsic pattern learning." Corr abs/1805.07291 (2018). Open Access Copy
 Lu, J, and Thicke, K. "Cubic scaling algorithms for RPA correlation using interpolative separable density fitting." Journal of Computational Physics 351 (December 15, 2017): 187202. Full Text Open Access Copy
 Cao, Y, and Lu, J. "Lindblad equation and its semiclassical limit of the AndersonHolstein model." Journal of Mathematical Physics 58, no. 12 (December 1, 2017). Full Text Open Access Copy
 Li, L, Liu, JG, and Lu, J. "Fractional Stochastic Differential Equations Satisfying FluctuationDissipation Theorem." Journal of Statistical Physics 169, no. 2 (October 1, 2017): 316339. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "A convergent method for linear halfspace kinetic equations." Esaim: Mathematical Modelling and Numerical Analysis 51, no. 5 (September 1, 2017): 15831615. Full Text Open Access Copy
 Lu, J, and Steinerberger, S. "A variation on the DonskerVaradhan inequality for the principal eigenvalue." Proceedings. Mathematical, Physical, and Engineering Sciences 473, no. 2204 (August 23, 2017): 20160877null. Full Text Open Access Copy
 Lu, J, and Yang, H. "A cubic scaling algorithm for excited states calculations in particle–particle random phase approximation." Journal of Computational Physics 340 (July 1, 2017): 297308. Full Text Open Access Copy
 Gao, Y, Liu, JG, and Lu, J. "Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces." Journal of Nonlinear Science 27, no. 3 (June 1, 2017): 873926. Full Text Open Access Copy
 Li, C, Lu, J, and Yang, W. "On extending KohnSham density functionals to systems with fractional number of electrons." The Journal of Chemical Physics 146, no. 21 (June 2017): 214109. Full Text
 Lu, J, and Thicke, K. "Orbital minimization method with ℓ^{1} regularization." Journal of Computational Physics 336 (May 1, 2017): 87103. Full Text Open Access Copy
 Huang, Y, Lu, J, and Ming, P. "A Hybrid Globallocal Numerical Method for Multiscale PDEs." (April 23, 2017). Open Access Copy
 Li, L, Liu, JG, and Lu, J. "Fractional stochastic differential equations satisfying fluctuationdissipation theorem." (April 23, 2017). Open Access Copy
 Lu, J, and Zhou, Z. "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. Full Text Open Access Copy
 Niu, X, Luo, T, Lu, J, and Xiang, Y. "Dislocation climb models from atomistic scheme to dislocation dynamics." Journal of the Mechanics and Physics of Solids 99 (February 1, 2017): 242258. Full Text Open Access Copy
 Watson, AB, Lu, J, and Weinstein, MI. "Wavepackets in inhomogeneous periodic media: Effective particlefield dynamics and Berry curvature." Journal of Mathematical Physics 58, no. 2 (February 2017): 021503021503. Full Text Open Access Copy
 Cornelis, B, Yang, H, Goodfriend, A, Ocon, N, Lu, J, and Daubechies, I. "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): 160171. Full Text Open Access Copy
 Gao, Y, Liu, JG, and Lu, J. "Weak solution of a continuum model for vicinal surface in the attachmentdetachmentlimited regime." Siam Journal on Mathematical Analysis 49, no. 3 (January 1, 2017): 17051731. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "Validity and Regularization of Classical HalfSpace Equations." Journal of Statistical Physics 166, no. 2 (January 1, 2017): 398433. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "Halfspace kinetic equations with general boundary conditions." Mathematics of Computation 86, no. 305 (January 1, 2017): 12691301. Full Text Open Access Copy
 Li, Q, and Lu, J. "An Asymptotic Preserving Method for Transport Equations with Oscillatory Scattering Coefficients." Multiscale Modeling & Simulation 15, no. 4 (January 2017): 16941718. Full Text Open Access Copy
 Li, XH, and Lu, J. "Quasinonlocal coupling of nonlocal diffusions." Siam Journal on Numerical Analysis 55, no. 5 (January 1, 2017): 23942415. Full Text Open Access Copy
 Lu, J, and Yang, H. "Preconditioning Orbital Minimization Method for Planewave Discretization." Multiscale Modeling & Simulation 15, no. 1 (January 2017): 254273. Full Text Open Access Copy
 Mendl, CB, Lu, J, and Lukkarinen, J. "Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory." Physical review. E 94, no. 61 (December 2, 2016): 062104. Full Text Open Access Copy
 Yu, TQ, Lu, J, Abrams, CF, and VandenEijnden, E. "Multiscale implementation of infiniteswap replica exchange molecular dynamics." Proceedings of the National Academy of Sciences of the United States of America 113, no. 42 (October 3, 2016): 1174411749. (Review) Full Text
 Lu, J, and Zhou, Z. "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. Full Text Open Access Copy
 Li, X, and Lu, J. "Traction boundary conditions for molecular static simulations." Computer Methods in Applied Mechanics and Engineering 308 (August 15, 2016): 310329. Full Text Open Access Copy
 Lin, L, and Lu, J. "Decay estimates of discretized Green’s functions for Schrödinger type operators." Science China Mathematics 59, no. 8 (August 1, 2016): 15611578. Full Text Open Access Copy
 Lai, R, and Lu, J. "Localized density matrix minimization and linearscaling algorithms." Journal of Computational Physics 315 (June 15, 2016): 194210. Full Text Open Access Copy
 Lu, J, and Ying, L. "Sparsifying preconditioner for soliton calculations." Journal of Computational Physics 315 (June 15, 2016): 458466. Full Text Open Access Copy
 Lu, J, Wirth, B, and Yang, H. "Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis." Journal of the Mechanics and Physics of Solids 89 (April 1, 2016): 194210. Full Text Open Access Copy
 Chen, J, and Lu, J. "Analysis 0f the divideandconquer method for electronic structure calculations." Mathematics of Computation 85, no. 302 (January 1, 2016): 29192938. Full Text Open Access Copy
 Delgadillo, R, Lu, J, and Yang, X. "Gaugeinvariant frozen Gaussian approximation method for the schrödinger equation with periodic potentials." Siam Journal on Scientific Computing 38, no. 4 (January 1, 2016): A2440A2463. Full Text Open Access Copy
 Li, C, Lu, J, and Yang, W. "Gentlest ascent dynamics for calculating first excited state and exploring energy landscape of KohnSham density functionals." The Journal of chemical physics 143, no. 22 (December 2015): 224110. Full Text
 Lu, J, Moroz, V, and Muratov, CB. "OrbitalFree Density Functional Theory of OutofPlane Charge Screening in Graphene." Journal of Nonlinear Science 25, no. 6 (December 1, 2015): 13911430. Full Text Open Access Copy
 Li, Q, Lu, J, and Sun, W. "Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics." Journal of Computational Physics 292 (July 1, 2015): 141167. Full Text Open Access Copy
 Yang, H, Lu, J, Brown, WP, Daubechies, I, and Ying, L. "Quantitative Canvas Weave Analysis Using 2D Synchrosqueezed Transforms: Application of timefrequency analysis to art investigation." Ieee Signal Processing Magazine 32, no. 4 (July 2015): 5563. Full Text Open Access Copy
 Lu, J, and Mendl, CB. "Numerical scheme for a spatially inhomogeneous matrixvalued quantum Boltzmann equation." Journal of Computational Physics 291 (June 5, 2015): 303316. Full Text Open Access Copy
 Lu, J, Liu, JG, and Margetis, D. "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). Full Text Open Access Copy
 Lu, J, and Nolen, J. "Reactive trajectories and the transition path process." Probability Theory and Related Fields 161, no. 12 (February 2015): 195244. Full Text Open Access Copy
 Lai, R, Lu, J, and Osher, S. "Density matrix minimization with ℓ1 regularization." Communications in Mathematical Sciences 13, no. 8 (January 1, 2015): 20972117. Full Text Open Access Copy
 Liu, J, Lu, J, and Zhou, X. "Efficient rare event simulation for failure problems in random media." Siam Journal on Scientific Computing 37, no. 2 (January 1, 2015): A609A624. Full Text Open Access Copy
 Lu, J, and Marzuola, JL. "Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics." Communications in Mathematical Sciences 13, no. 5 (January 1, 2015): 10511074. Full Text Open Access Copy
 Lu, J, and Ying, L. "Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost." Journal of Computational Physics 302 (2015): 329335. Full Text Open Access Copy
 Yang, H, Lu, J, and Ying, L. "Crystal image analysis using 2D synchrosqueezed transforms." Multiscale Modeling and Simulation 13, no. 4 (January 1, 2015): 15421572. Full Text Open Access Copy
 Lu, J, and Otto, F. "Nonexistence of a Minimizer for ThomasFermiDiracvon Weizsäcker Model." Communications on Pure and Applied Mathematics 67, no. 10 (October 2014): 16051617. Full Text
 Yang, Y, Peng, D, Lu, J, and Yang, W. "Excitation energies from particleparticle random phase approximation: Davidson algorithm and benchmark studies." The Journal of Chemical Physics 141, no. 12 (September 28, 2014): 124104124104. Full Text
 Lu, J, and VandenEijnden, E. "Exact dynamical coarsegraining without timescale separation." The Journal of Chemical Physics 141, no. 4 (July 28, 2014): 044109044109. Full Text
 E, W, and Lu, J. "Mathematical theory of solids: From quantum mechanics to continuum models." Discrete and Continuous Dynamical Systems 34, no. 12 (June 2014): 50855097. Full Text
 Kohn, RV, Lu, J, Schweizer, B, and Weinstein, MI. "A variational perspective on cloaking by anomalous localized resonance." Communications in Mathematical Physics 328, no. 1 (March 14, 2014): 127. Full Text Open Access Copy
 Lin, L, Lu, J, and Shao, S. "Analysis of time reversible bornoppenheimer molecular dynamics." Entropy 16, no. 1 (January 1, 2014): 110137. Full Text Open Access Copy
 Lu, J, and Ming, P. "Stability of a forcebased hybrid method with planar sharp interface." Siam Journal on Numerical Analysis 52, no. 4 (January 1, 2014): 20052026. Full Text Open Access Copy
 Lu, J, and Otto, F. "Nonexistence of a minimizer for ThomasFermiDiracvon Weizsäcker model." Communications on Pure and Applied Mathematics 67, no. 10 (2014): 16051617. Full Text
 Lu, J, and VandenEijnden, E. "Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials." J Chem Phys 138, no. 8 (February 28, 2013): 084105. Full Text Open Access Copy Link to Item
 E, W, Lu, J, and Yao, Y. "The landscape of complex networks: Critical nodes and a hierarchical decomposition." Methods and Applications of Analysis 20, no. 4 (2013): 383404. Full Text
 E, W, Lu, JF, and Yang, X. "Asymptotic analysis of quantum dynamics in crystals: The BlochWigner transform, Bloch dynamics and Berry phase." Acta Mathematicae Applicatae Sinica 29, no. 3 (2013): 465476. Full Text
 Lu, J, and Ming, P. "Convergence of a ForceBased Hybrid Method in Three Dimensions." Communications on Pure and Applied Mathematics 66, no. 1 (January 2013): 83108. Full Text Open Access Copy
 E, W, and Lu, J. "Stability and the continuum limit of the spinpolarized ThomasFermiDiracvon Weizsäcker model." Journal of Mathematical Physics 53, no. 11 (November 2012): 115615115615. Full Text Open Access Copy
 Lu, J, and Yang, X. "Frozen gaussian approximation for general linear strictly hyperbolic systems: Formulation and eulerian methods." Multiscale Modeling and Simulation 10, no. 2 (September 7, 2012): 451472. Full Text Open Access Copy
 Lu, J, and Yang, X. "Convergence of frozen Gaussian approximation for highfrequency wave propagation." Communications on Pure and Applied Mathematics 65, no. 6 (June 1, 2012): 759789. Full Text Open Access Copy
 Lin, L, Lu, J, Ying, L, and E, W. "Optimized local basis set for Kohn–Sham density functional theory." Journal of Computational Physics 231, no. 13 (May 2012): 45154529. Full Text
 Lin, L, Lu, J, Ying, L, and E, W. "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): 21402154. Full Text Open Access Copy
 E, W, and Lu, J. "The KohnSham equation for deformed crystals." Memoirs of the American Mathematical Society 221, no. 1040 (2012): 11. Full Text
 Schütte, C, Noé, F, Lu, J, Sarich, M, and VandenEijnden, E. "Markov state models based on milestoning." The Journal of Chemical Physics 134, no. 20 (May 28, 2011): 204105204105. Full Text
 Lin, L, Lu, J, and Ying, L. "Fast construction of hierarchical matrix representation from matrixvector multiplication." Journal of Computational Physics 230, no. 10 (May 10, 2011): 40714087. Full Text Open Access Copy
 Daubechies, I, Lu, J, and Wu, HT. "Synchrosqueezed wavelet transforms: An empirical mode decompositionlike tool." Applied and Computational Harmonic Analysis 30, no. 2 (March 2011): 243261. Full Text
 E, W, and Lu, J. "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): 407433. Full Text
 Lin, L, Yang, C, Meza, JC, Lu, J, Ying, L, and E, W. "SelInvAn Algorithm for Selected Inversion of a Sparse Symmetric Matrix." Acm Transactions on Mathematical Software 37, no. 4 (February 1, 2011): 119. Full Text
 E, W, Lu, J, and Yang, X. "Effective Maxwell equations from timedependent density functional theory." Acta Math. Sin. 32 (2011): 339339. Open Access Copy
 Lin, L, Yang, C, Lu, J, Ying, L, and E, W. "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): 13291351. Full Text
 Lu, J, and Yang, X. "Frozen Gaussian approximation for high frequency wave propagation." Communications in Mathematical Sciences 9, no. 3 (2011): 663683. Open Access Copy
 E, W, and Lu, J. "Electronic structure of smoothly deformed crystals: Cauchyborn rule for the nonlinear tightbinding model." Communications on Pure and Applied Mathematics 63, no. 11 (November 2010): 14321468. Full Text
 E, W, Li, T, and Lu, J. "Localized bases of eigensubspaces and operator compression." Proceedings of the National Academy of Sciences 107, no. 4 (January 26, 2010): 12731278. Full Text
 Lin, L, Lu, J, Car, R, and E, W. "Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems." Physical Review B 79, no. 11 (March 2009). Full Text Open Access Copy
 Lin, L, Lu, J, Ying, L, Car, R, and E, W. "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): 755777.
 Lin, L, Lu, J, Ying, L, and E, W. "Polebased approximation of the FermiDirac function." Chin. Ann. Math. Ser. B 30 (2009): 729742. Open Access Copy
 GarciaCervera, CJ, Ren, W, Lu, J, and E, W. "Sequential multiscale modelling using sparse representation." Commun. Comput. Phys. 4 (2008): 10251033.
 E, W, and Lu, J. "The Elastic Continuum Limit of the Tight Binding Model*." Chinese Annals of Mathematics, Series B 28, no. 6 (December 2007): 665676. Full Text
 E, W, GarcíaCervera, CJ, and Lu, J. "A sublinear scaling algorithm for computing the electronic structure of materials." Communications in Mathematical Sciences 5, no. 4 (2007): 9991026. Full Text
 E, W, and Lu, J. "Seamless multiscale modeling via dynamics on fiber bundles." Communications in Mathematical Sciences 5, no. 3 (2007): 649663. Full Text
 E, W, and Lu, J. "The continuum limit and QMcontinuum approximation of quantum mechanical models of solids." Communications in Mathematical Sciences 5, no. 3 (2007): 679696. Full Text
 An, D, HeadGordon, T, Lin, L, and Lu, J. "Convergence of Stochasticextended Lagrangian molecular dynamics method for polarizable force field simulation." . Link to Item
 Cai, Z, Lu, J, and Stubbs, K. "On discrete Wigner transforms." . Open Access Copy Link to Item
 Cai, Z, Lu, J, and Yang, S. "Inchworm Monte Carlo method for open quantum systems." . Link to Item
 Cao, Y, Lu, J, and Lu, Y. "Exponential decay of Rényi divergence under FokkerPlanck equations." . Link to Item
 Cao, Y, Lu, J, and Lu, Y. "Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNSdetailed balance." . Link to Item
 Cao, Y, and Lu, J. "Tensorization of the strong data processing inequality for quantum chisquare divergences." . Link to Item
 Chen, H, Li, Q, and Lu, J. "A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer." . Link to Item
 Chen, K, Li, Q, Lu, J, and Wright, SJ. "Randomized sampling for basis functions construction in generalized finite element methods." . Open Access Copy Link to Item
 Chen, K, Li, Q, Lu, J, and Wright, SJ. "Random Sampling and Efficient Algorithms for Multiscale PDEs." . Link to Item
 E, W, Lu, J, and Yang, JZ. "Uniform accuracy of the quasicontinuum method(Published online)." Physical Review B 74, no. 21. Full Text
 E, W, and Lu, J. "Multiscale modeling(Published online)." Scholarpedia 6, no. 10: 1152711527. Full Text
 Gao, Y, Liu, JG, Lu, J, and Marzuola, JL. "Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects." . Link to Item
 GarcíaCervera, CJ, Lu, J, Xuan, Y, and E, W. "Linearscaling subspaceiteration algorithm with optimally localized nonorthogonal wave functions for KohnSham density functional theory(Published online)." Physical Review B 79, no. 11. Full Text
 Holst, M, Hu, H, Lu, J, Marzuola, JL, Song, D, and Weare, J. "Symmetry Breaking in Density Functional Theory due to Dirac Exchange for a Hydrogen Molecule." . Link to Item
 Khoo, Y, Lu, J, and Ying, L. "Solving parametric PDE problems with artificial neural networks." Open Access Copy Link to Item
 Khoo, Y, Lu, J, and Ying, L. "Efficient construction of tensor ring representations from sampling." Open Access Copy Link to Item
 Khoo, Y, Lu, J, and Ying, L. "Solving for high dimensional committor functions using artificial neural networks." Link to Item
 Li, L, Li, Y, Liu, JG, Liu, Z, and Lu, J. "A stochastic version of Stein Variational Gradient Descent for efficient sampling." . Link to Item
 Li, L, Lu, J, Mattingly, J, and Wang, L. "Numerical methods for stochastic differential equations based on Gaussian mixture." . Open Access Copy Link to Item
 Li, X, Lin, L, and Lu, J. "PEXSI$Σ$: A Green's function embedding method for KohnSham density functional theory." Open Access Copy Link to Item
 Li, Y, Cheng, X, and Lu, J. "ButterflyNet: Optimal Function Representation Based on Convolutional Neural Networks." . Open Access Copy Link to Item
 Li, Y, Lu, J, and Mao, A. "Variational training of neural network approximations of solution maps for physical models." . Link to Item
 Li, Y, Lu, J, and Wang, Z. "Coordinatewise descent methods for leading eigenvalue problem." . Link to Item
 Lu, J, Sachs, M, and Steinerberger, S. "Quadrature Points via Heat Kernel Repulsion." . Link to Item
 Lu, J, Sogge, CD, and Steinerberger, S. "Approximating Pointwise Products of Laplacian Eigenfunctions." . Link to Item
 Lu, J, Watson, AB, and Weinstein, MI. "Dirac operators and domain walls." . Link to Item
 Lu, J, and Otto, F. "An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus." Open Access Copy Link to Item
 Lu, J, and Otto, F. "Optimal artificial boundary condition for random elliptic media." Link to Item
 Lu, J, and Steinerberger, S. "Detecting localized eigenstates of linear operators." Open Access Copy Link to Item
 Lu, J, and Steinerberger, S. "Riesz Energy on the Torus: Regularity of Minimizers." Open Access Copy Link to Item
 Lu, J, and Steinerberger, S. "On Pointwise Products of Elliptic Eigenfunctions." . Link to Item
 Lu, J, and Steinerberger, S. "A DimensionFree HermiteHadamard Inequality via Gradient Estimates for the Torsion Function." . Link to Item
 Lu, J, and Wang, Z. "The full configuration interaction quantum Monte Carlo method in the lens of inexact power iteration." Open Access Copy Link to Item
 Lu, J, and Yang, H. "Preconditioning Orbital Minimization Method for Planewave Discretization." . Open Access Copy
 Lu, J, and Ying, L. "Fast algorithm for periodic density fitting for Bloch waves." Open Access Copy Link to Item
 Lu, J, and Zhou, Z. "Bloch dynamics with second order Berry phase correction." Open Access Copy Link to Item
 Lu, J, and Zhou, Z. "Continuum limit and preconditioned Langevin sampling of the path integral molecular dynamics." . Link to Item
 Nishimura, A, Dunson, D, and Lu, J. "Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods." . Link to Item
 Nolen, JH, Lu, J, and Lu, Y. "Scaling limit of the Stein variational gradient descent: the mean field regime(Accepted)." Siam Journal on Mathematical Analysis . Link to Item
 Thicke, K, Watson, A, and Lu, J. "Computation of bound states of semiinfinite matrix Hamiltonians with applications to edge states of twodimensional materials." . Link to Item

Conference Papers
 Yu, V, Huhn, W, Lin, L, Lu, J, VazquezMayagoitia, A, Yang, C, and Blum, V. "ELSI: A unified software interface for KohnSham electronic structure solvers." 255th National Meeting and Exposition of the AmericanChemicalSociety (ACS)  Nexus of Food, Energy, and Water. New Orleans, LA. March 18, 2018  March 22, 2018.: AMER CHEMICAL SOC, March 18, 2018. Link to Item
 Xian, Y, Thompson, A, Qiu, Q, Nolte, L, Nowacek, D, Lu, J, Calderbank, R, and IEEE, . "CLASSIFICATION OF WHALE VOCALIZATIONS USING THE WEYL TRANSFORM." 2015. Link to Item

 Teaching & Mentoring

Recent Courses
 MATH 375: Introduction to Linear Programming and Game Theory 2019
 MATH 660: Numerical Partial Differential Equations 2019
 MATH 757: Introduction to Linear Programming and Game Theory 2019
 MATH 69070: Topics in Applied Mathematics 2018
 MATH 79090: Minicourse in Advanced Topics 2018
 MATH 356: Elementary Differential Equations 2017
 MATH 631: Measure and Integration 2017
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