Kui Ren's Homepage

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):

· Error analysis for the implicit boundary integral method (with Y. Zhong, O. Runborg, and R. Tsai), BIT Numer. Math., 65, 8, 2025. [pdf].

· A three-stage method for reconstructing multiple coefficients in coupled photoacoustic and diffuse optical imaging (with Y. Pan and S. Tong), Inverse Problems, 41, 035008, 2025. [pdf]

· An energy-based discontinuous Galerkin method for the nonlinear Schrödinger equation with wave operator (with L. Zhang and Y. Zhou), SIAM J. Numer. Anal. 62, 2459-2483, 2024. [pdf]

· An explicit spectral decomposition of the ADRT (with W. Li and D. Rim), Submitted, 2024. [pdf]

· Sampling with Adaptive Variance for Multimodal Distributions (with B. Engquist and Y. Yang), Submitted, 2024. [pdf]

· Phase retrieval via media diversity (with Y. Cheng and N. Soedjak), Submitted, 2024. [pdf]

· A Policy Iteration Method for Inverse Mean Field Games (with N. Soedjak and S. Tong), Submitted, 2024. [pdf]

· Reconstructing a state-independent cost function in a mean-field game model (with N Soedjak, K. Wang and H. Zhai), Inverse Problems, 40, 105010, 2024. [pdf]

· Fourier-Based Bounds for Wasserstein Distances and Their Implications in Computational Inversion (with W. Hong and V. A. Kobzar), NeurIPS 2023 Workshop Optimal Transport and Machine Learning, 2023. [pdf]

· Unique determination of cost functions in a multipopulation mean field game model (with N. Soedjak and K. Wang), J. Diff. Eqn, 427, 843-867, 2025. [pdf]

· A range characterization of the single-quadrant ADRT (with W. Li and D. Rim), Math. Comput., 92, 283-306, 2024. [pdf]

· Recovering coefficients in a system of semilinear Helmholtz equations from internal data (with Nathan Soedjak), Inverse Problems, 40, 045023, 2024. [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., 83, 1677-1695, 2023. [pdf].

· Adaptive State-Dependent Diffusion for Derivative-Free Optimization (with B. Engquist and Y. Yang), Commun. Appl. Math. Comput., 6, 1241-1269, 2024.[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].

· A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems (with L. Zhang), Submitted, 2025. [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, 127, e2021JB023830, 2022. [pdf].

· An algebraically converging stochastic gradient algorithm for global optimization (with B. Engquist and Y. Yang), Commun. Math. Sci., 2025. [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., 82, 602-624, 2021. [pdf].

· A range characterization of the single-quadrant ADRT (with W. Li and D. Rim), Math. Comput., 92: 283-306, 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: 5613-5645, 2021. [pdf].

· Unique determination of absorption coefficients in a semilinear transport equation (with Y. Zhong), SIAM J. Math. Anal., 53: 5158-5184, 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 P₂ 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.

Last updated: July 2018

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