# Jianfeng Lu

- Associate Professor of Mathematics
- Associate Professor of Physics (Secondary)
- Associate Professor of Chemistry (Secondary)
- Associate Professor in Physics (Secondary)

**External address:**242 Physics Bldg, 120 Science Drive, Durham, NC 27708

**Internal office address:**Mathematics Department, Duke University, Box 90320, Durham, NC 27708

**Phone:**(919) 660-2875

##### Links

### Research Areas and Keywords

##### Analysis

electronic structure models, calculus of variations, semiclassical analysis

##### Computational Mathematics

electronic structure models, multiscale modeling and simulations, numerical analysis, rare events simulation, computational physics, time-frequency analysis, fast algorithms, stochastic numerical methods, kinetic equations, nonlinear Schrodinger equations, quantum chemistry, computational statistical mechanics, optimization, high frequency wave propagation

##### Mathematical Physics

electronic structure models, quantum chemistry, kinetic theory, quantum information

##### PDE & Dynamical Systems

multiscale modeling and simulations, numerical analysis, calculus of variations, kinetic equations, Schroedinger equations

##### Physical Modeling

electronic structure models, multiscale modeling and simulations, rare events simulation, computational physics, kinetic equations, nonlinear Schroedinger equations, quantum chemistry, computational statistical mechanics

##### Probability

rare events simulation, computational statistical mechanics, stochastic numerical methods

##### Signals, Images & Data

time-frequency analysis, fast algorithms, optimization, applied harmonic analysis

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.

### Selected Grants

FET: Small: Efficient Inference Tools for Quantum Systems: Algorithms, Applications, and Analysis awarded by National Science Foundation (Co-Principal Investigator). 2019 to 2022

HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by National Science Foundation (Co-Principal Investigator). 2019 to 2022

Quantum Computing in Chemical and Material Sciences awarded by Department of Energy (Co-Principal Investigator). 2018 to 2021

Collaborative Research: SI2-SSI: ELSI-Infrastructure for Scalable Electronic Structure Theory awarded by National Science Foundation (Co-Principal Investigator). 2015 to 2021

CAREER: Research and training in advanced computational methods for quantum and statistical mechanics awarded by National Science Foundation (Principal Investigator). 2015 to 2020

Mathematical Problems for Electronic Structure Models awarded by National Science Foundation (Principal Investigator). 2013 to 2016

Li, Y., et al. “Variational training of neural network approximations of solution maps for physical models.” *Journal of Computational Physics*, vol. 409, May 2020. *Scopus*, doi:10.1016/j.jcp.2020.109338.
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Lu, J., et al. “Quadrature Points via Heat Kernel Repulsion.” *Constructive Approximation*, vol. 51, no. 1, Feb. 2020, pp. 27–48. *Scopus*, doi:10.1007/s00365-019-09471-4.
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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*, vol. 148, no. 2, Jan. 2020, pp. 673–79. *Scopus*, doi:10.1090/proc/14843.
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Lu, J., et al. “Dirac operators and domain walls.” *Siam Journal on Mathematical Analysis*, vol. 52, no. 2, Jan. 2020, pp. 1115–45. *Scopus*, doi:10.1137/19M127416X.
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Cai, Z., et al. “Inchworm Monte Carlo Method for Open Quantum Systems.” *Communications on Pure and Applied Mathematics*, Jan. 2020. *Scopus*, doi:10.1002/cpa.21888.
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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*, vol. 42, no. 1, Jan. 2020, pp. B1–29. *Scopus*, doi:10.1137/18M1166626.
Full Text Open Access Copy

Lu, J., and S. Steinerberger. “Optimal Trapping for Brownian Motion: a Nonlinear Analogue of the Torsion Function.” *Potential Analysis*, Jan. 2020. *Scopus*, doi:10.1007/s11118-020-09845-5.
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Chen, H., et al. “A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer.” *Journal of Computational Physics*, vol. 398, Dec. 2019. *Scopus*, doi:10.1016/j.jcp.2019.108893.
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Lu, J., et al. “Approximating pointwise products of Laplacian eigenfunctions.” *Journal of Functional Analysis*, vol. 277, no. 9, Nov. 2019, pp. 3271–82. *Scopus*, doi:10.1016/j.jfa.2019.05.025.
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Cao, Y., et al. “Exponential Decay of Rényi Divergence Under Fokker–Planck Equations.” *Journal of Statistical Physics*, vol. 176, no. 5, Sept. 2019, pp. 1172–84. *Scopus*, doi:10.1007/s10955-019-02339-8.
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## Pages

Yu, Victor, et al. “Large-scale benchmark of electronic structure solvers with the ELSI infrastructure.” *Abstracts of Papers of the American Chemical Society*, vol. 257, AMER CHEMICAL SOC, 2019.

Yu, Victor, et al. “ELSI: A unified software interface for Kohn-Sham electronic structure solvers.” *Abstracts of Papers of the American Chemical Society*, vol. 255, AMER CHEMICAL SOC, 2018.

Xian, Yin, et al. “CLASSIFICATION OF WHALE VOCALIZATIONS USING THE WEYL TRANSFORM.” *2015 Ieee International Conference on Acoustics, Speech, and Signal Processing (Icassp)*, 2015, pp. 773–77.

A key goal of *Together Duke* is to invest in faculty as scholars and leaders of the university’s intellectual communities. To foster collaboration around new and emerging areas of interest... read more »

The 2017 IMA Prize in Mathematics and its Applications has been awarded to Jianfeng Lu, an associate professor in the Department of Mathematics at Duke University, with secondary appointments in the Departments of Chemistry and Physics. Lu received... read more »

New faculty member applies math to solve some of the hardest questions in science Durham, NC - As a mathematician, Jianfeng Lu appreciates the abstract beauty of theories and proofs. But he also sees his craft as a powerful, pragmatic tool for... read more »