Kui Ren Professor of
Applied Mathematics 215 S. W. Mudd Building 500 W 120^{th} Street New York, NY 20017 Tel: 2128544731 Email: kr2002@columbia.edu 
Welcome to submissions: SIAM Conference on
Imaging Science (IS24) Inverse
Problems Special Issue: Computational
Optimal Transport Theory for Inverse Problems SIAM
Journal on Applied Mathematics SIAM:
Multiscale Modeling and Simulation Journal of Computational Mathematics 


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):
· Recovering
coefficients in a system of semilinear Helmholtz equations from internal data (with Nathan Soedjak), Submitted, 2023. [pdf].
· Transport models
for wave propagation in scattering media with nonlinear absorption (with J. Kraisler, W. Li, J.C.Schotland and Y.
Zhong), SIAM J. Appl. Math., 2023. [pdf].
· Adaptive
StateDependent Diffusion for DerivativeFree Optimization (with B. Engquist and Y. Yang), Submitted, 2022. [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. [pdf].
· Datadriven joint
inversion for PDE models (with L. Zhang), Submitted, 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), Submitted,
2022. [pdf].
· Coupling deep learning
with full waveform inversion (with W.
Ding and Lu. Zhang), Submitted, 2022.
[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 singlequadrant ADRT (with W. Li and D. Rim), Math.
Comput., 92: 283306, 2023.
[pdf].
· Separability of
the kernel function in an integral formulation for anisotropic radiative
transfer (with H. Zhao and Y. Zhong), SIAM
J. Math. Anal., 53: 56135645, 2021. [pdf].
· Unique
determination of absorption coefficients in a semilinear transport equation (with Y. Zhong), SIAM J. Math. Anal., 53:
51585184, 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., 359:199215, 2018. [pdf].
· Image reconstruction in
quantitative PAT with the simplified P_{2} model (with
C. Frederick and S. Vallelian), SIAM J. Imag. Sci., 11:28472876, 2018.
[pdf].
· Characterizing the impact of
model uncertainties in quantitative photoacoustics (with S. Vallelian), SIAM/ASA
J Uncertainty Quantification,
8:636667, 2020. [pdf].
· Surface effects in dense random graphs with sharp edge constraint (with C. Radin and L. Sadun), Preprint, 2017. [pdf].
· Quantitative photoacoustic imaging of twophoton absorption, (with P. Bardsley and R. Zhang), J. Biomed. Opt., 23, 016002, 2018. [pdf].
· A global stability estimate for the photoacoustic 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 twophoton absorption (with R. Zhang), SIAM J. Appl. Math., 78, 479503, 2018. [pdf].
· A symmetry breaking transition in the edge/triangle network model (with C. Radin and L. Sadun), AIHPD, 5:251286, 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, 140167, 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, 136,
2016. [pdf].
· On the modeling and simulation of reactiontransfer dynamics in semiconductorelectrolyte solar cells (with Y. He, I. M. Gamba and H. Lee), SIAM J. Appl. Math., 75, 25152539, 2015. [pdf].
· A onestep 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, 233258, 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, 201234, 2014. [pdf].
· Inverse transport calculations in optical imaging with subspace optimization algorithms (with T. Ding), J. Comput. Phys., 273, 212226, 2014 [pdf]
· Quantitative fluorescence photoacoustic tomography (with H. Zhao), SIAM J Imag. Sci., 6, 24042429, 2013. [pdf]
· A hybrid reconstruction method for quantitative PAT (with H. Gao and H. Zhao), SIAM J. Imag. Sci., 6, 3255, 2013. [pdf]
· On multispectral 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.
This webpage has been visited times since 2008. 