Kui Ren

Professor of Applied
Mathematics

Department
of Applied Physics & Applied Mathematics

215 S. W. Mudd Building

500 W 120^{th} Street

New York, NY 20017

Tel: 212-854-4731

Email: kr2002@columbia.edu

I am a faculty member in the Applied Mathematics Program. I also a member of the Data Science Institute, the Initiative for Computational Science and Engineering, and the Artificial Intelligence @Columbia

Seminars @ Columbia: Applied
Math Colloquium Applied
Probability Seminar Statistics
Seminar Mathematics Colloquium

I am
interested in applied and computational mathematics in general. My recent
research topics include: applied PDE, computational inverse problems,
mathematics of imaging, computational learning, numerical optimization, fast
algorithms, random graphs and complex networks.

Here are some recent preprints/reprints (a full list can be found here; some of the simplified versions of the computational codes we developed can be found at Github):

· Separability of
the kernel function in an integral formulation for anisotropic radiative
transfer (with H. Zhao and Y. Zhong), *SIAM J. Math. Anal., *2021. [pdf].

· A generalized weighted
optimization method for computational learning and inversion (with B. Engquist and Y.
Yang), *The 39th International Conference
on Learning Representations (ICLR 2022)*, 2022. [pdf].

· Deep neural network
for creating reliable PmP database with a case study
in Southern California (with W. Ding,
T. Li, X. Yang, and P. Tong), *J. Geophys. Res*, 2022. [pdf].

· An algebraically
converging stochastic gradient algorithm for global optimization (with B. Engquist and Y.
Yang), 2021. [pdf].

· Coupling deep learning
with full waveform inversion (with W.
Ding and Lu. Zhang), *Submitted*,* *2021.
[pdf].

· Inverse transport
and diffusion problems in photoacoustic imaging with nonlinear absorption (with R.-Y. Lai and T. Zhou), *SIAM J. Appl.
Math., *2021. [pdf].

· A range
characterization of the single-quadrant ADRT (with W. Li and D. Rim), *Math. Comput.*, 2022.
[pdf].

· Unique
determination of absorption coefficients in a semilinear
transport equation (with Y. Zhong), *SIAM J. Math. Anal., *2021. [pdf].

· Imaging point sources
in heterogeneous (with Y. Zhong), *Inverse Problems*, 35: 125003, 2019. [pdf].

· The quadratic
Wasserstein metric for inverse data matching, *Inverse Problems*,
36:055001, 2020*.* [pdf].

· A fast algorithm for
radiative transport in isotropic media (with R. Zhang and Y. Zhong), *J. Comput. Phys.*, 2019. [pdf].

· An implicit boundary integral method for computing electric potential
of macromolecules in solvent (with R. Tsai and Y. Zhong), *J. Comput. Phys., *359:199-215,
2018. [pdf].

· Image reconstruction in
quantitative PAT with the simplified P_{2} model (with
C. Frederick and S. Vallelian), *SIAM J. Imag. Sci., *11:2847-2876, 2018. [pdf].

· Characterizing the impact of
model uncertainties in quantitative photoacoustics
(with S. Vallelian), *SIAM/ASA J Uncertainty
Quantification**, *8:636-667, 2020. [pdf].

· Surface effects in
dense random graphs with sharp edge constraint (with C. Radin
and L. Sadun), *Preprint, *2017. [pdf].

· Quantitative
photo-acoustic imaging of two-photon absorption, (with P. Bardsley
and R. Zhang), *J. Biomed. Opt.*, 23, 016002, 2018. [pdf].

· A global stability
estimate for the photo-acoustic inverse problem in layered media, (with F. Triki), *European J. Appl. Math., *In Press, 2018. [pdf].

· The phases of large
networks with edge and triangle constraints, (with R. Kenyon, C. Radin and L. Sadun), *J. Phys.
A: Math. Theor.*, 50, 435001, 2017. [pdf].

· Nonlinear quantitative
photoacoustic tomography with two-photon absorption (with R. Zhang), *SIAM J.
Appl. Math.*, 78, 479-503, 2018. [pdf].

· A symmetry breaking
transition in the edge/triangle network model (with C. Radin
and L. Sadun), *AIHP-D*, 5:251-286, 2018. [pdf].

· Numerical algorithms
based on Galerkin methods for the modeling of
reactive interfaces in photoelectrochemical (PEC) solar cells (with M. Harmon
and I. M. Gamba), *J. Comput.
Phys.*, 327, 140-167, 2016. [pdf
].

· Inverse transport
problems in quantitative PAT for molecular imaging (with R. Zhang and Y.
Zhong), *Inverse Problems,* 31,
125012, 2015. [pdf].

· Bipodal structure in oversaturated random graphs (with R.
Kenyon, C. Radin and L. Sadun),
*Int. Math. Res. Notices*, 2016, 1-36, 2016. [pdf].

· On the modeling and
simulation of reaction-transfer dynamics in semiconductor-electrolyte solar
cells (with Y. He, I. M. Gamba and H. Lee), *SIAM
J. Appl. Math.,* 75, 2515-2539,
2015. [pdf].

· A one-step
reconstruction algorithm for quantitative photoacoustic imaging (with T. Ding
and S. Vallelian), *Inverse Problems,* 31, 095005, 2015. [pdf]. This paper was selected as by Inverse
Problems as one of the papers in its collection: Highlight
of 2015

· Multipodal Structure and Phase Transitions in Large Constrained Graphs (with R.
Kenyon, C. Radin and L. Sadun),
*J. Stat. Phys., *168, 233-258, 2017. [pdf].

· The Asymtotics
of Large Constrained Graphs (with C. Radin and L. Sadun), *J. Phys. A:
Math. Theor.* 47**,** 175001*,
*2014. [pdf]. One figure in the paper appears on the cover of the
journal.

· Quantitative
photoacoustic imaging in the radiative transport regime (with A. Mamonov), *Commun**. Math.
Sci*, 12, 201-234, 2014. [pdf].

· Inverse transport
calculations in optical imaging with subspace optimization algorithms (with T.
Ding), *J. Comput. Phys., *273, 212-226, 2014 [pdf]

· Quantitative fluorescence
photoacoustic tomography (with H. Zhao), *SIAM
J Imag. Sci.*, 6, 2404-2429, 2013. [pdf]

· A hybrid reconstruction
method for quantitative PAT (with H. Gao and H. Zhao), *SIAM J. Imag. Sci.*, 6, 32-55, 2013. [pdf]

· On multi-spectral
quantitative photoacoustic tomography (with
G. Bal), *Inverse Problems*, 28, 025010, 2012. [pdf]. This paper was selected as a featured article by
Inverse Problems and then chosen to be
included in its collection Highlight
of 2012

If you
have a PhD in mathematics but forget already who your thesis advisor was, you
can probably figure it out here.

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