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Recent research interests:

1. Inverse problems for partial differential equations

2. Mathematical analysis of emerging imaging methods

3. Mathematical modeling and numerical simulations with kinetic equations

4. Fast numerical algorithms for PDE based simulations

5. Random graphs, complex networks and related applications

 

General computational inversion and learning:

·        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].

·       Adaptive State-Dependent Diffusion for Derivative-Free Optimization (with B. Engquist and Y. Yang), Submitted, 2022. [pdf].

·       Data-driven joint inversion for PDE models (with L. Zhang), Submitted, 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].

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

 

Hybrid multi-physics inverse problems:

 

·       Unique determination of absorption coefficients in a semilinear transport equation (with Y. Zhong), Submitted, 2020. [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].

·       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), Euro. J. Appl. Math., 11, 2018. [pdf].

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

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

·       Quantitative photoacoustic imaging in the radiative transport regime (with A. Mamonov), Commun. Math. Sci., 12, 201-234, 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 included in its Highlight of 2012 collection.

·       Quantitative Thermo-acoustics and related problems (with G. Bal, G. Uhlmann and T. Zhou), Inverse Problems, 27, 055007, 2011. [pdf].

·       Multiple-source quantitative photoacoustic tomography (with G. Bal), Inverse Problems, 27, 075003, 2011. [pdf]. Read the news about this paper from Inverse Problems.

·       Non-uniqueness result for a hybrid inverse problem (with G. Bal), Contemporary Mathematics, 559, 29-38, 2011. [pdf].

 

Inverse boundary value problems:

 

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

·       Recovering doping profiles in semiconductor devices with the Boltzmann-Poisson model (with Y. Cheng and I. M. Gamba), J. Comput. Phys., 230, 3391-3412, 2011. [pdf].

·       Recent development in numerical techniques for transport-based medical imaging methods, Commun. Comput. Phys., 8, 1-50, 2010. [pdf].

·       Parametric image reconstruction using the discrete cosine transform for optical tomography (with X. Gu, J. Masciotti and A. H. Hilescher), J. Biomed. Opt., 14, 064003, 2009. [pdf].

·       Transport- and diffusion-based optical tomography in small domain: A comparative study (with G. Bal and A. H. Hilescher), Applied Optics, 46, 6669-6679, 2007. [pdf].

·       Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer (with X. Gu and A. Hielscher), Appl. Optics, 46, 1624-1632, 2007. [pdf].

·       Frequency domain optical tomography based on the equation of radiative transfer (with G. Bal and A. H. Hielscher), SIAM J. Sci. Comput., 28, 1463-1489, 2006. [pdf].

·       Reconstruction of singular surfaces by shape sensitivity analysis and level set method (with G. Bal), Math. Models Methods Appl. Sci. (M3AS), 16, 1347-1373, 2006. [pdf].

·       Inverse Problems in Transport and Diffusion Theory with Applications in Optical Tomography, PhD thesis, Columbia University, New York, 2006. [pdf].

·       Optical tomographic imaging as a PDE-constrained optimization problem (with G. Abdoulaev and A. H. Hielscher), Inverse Problems, 21, 1507-1530, 2005. [pdf].

·       Atmospheric concentration profile reconstructions from radiation measurements (with G. Bal), Inverse Problems, 21, 153-168, 2005. [pdf].

·       Frequency-domain tomography in small animals with the equation of radiative transfer (with B. Moa-Anderson, G.~Bal, X.~Gu, and A. H. Hielscher), Optical Tomography and Spectroscopy of Tissue VI (Edited by B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca), 111-120. SPIE, 2005, [pdf].

 

Uncertainty Characterization in Inverse Problems:

·       Characterizing impacts of model uncertainties in quantitative photoacoustics (with S. Vallelian), SIAM/ASA J. Uncertain. Quantif., 2020. [pdf].

·       Physics-based models for measurement correlations. Application to an inverse Sturm-Liouville problem (with G. Bal), Inverse Problems, 25, 055006, 2009. [pdf].

 

Imaging in complex (/random) media:

 

·       Imaging point sources in heterogeneous environments (with Y. Zhong), Inverse Problems, 2019. [pdf].

·       Transport-based imaging in random media (with G. Bal), SIAM Applied Math., 68, 1738-1762, 2008. [pdf].

·       Experimental validation of a transport-based imaging method in highly scattering environments (with G. Bal, L. Carin and D. Liu), Inverse Problems, 23, 2527-2539, 2007.  [pdf].

 

Kinetic modeling and simulations:

·       Transport models for wave propagation in scattering media with nonlinear absorption (with J. Kraisler, W. Li, J.C.Schotland and Y. Zhong), Submitted, 2022. [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 ]

·       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].

·       Generalized diffusion model in optical tomography with clear layers (with G. Bal), J. Opt. Soc. Am. A, 20, 2355-2364, 2003. [pdf].

 

Fast algorithms in scientific computing:

 

·       A range characterization of the single-quadrant ADRT(with W. Li and D. Rim), Submitted, 2020. [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].

·       Separability of the kernel function in an integral formulation for anisotropic radiative transfer (with H. Zhao and Y.), Submitted, 2019. [pdf].

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

·       Algorithm for solving the equation of radiative transfer in the frequency domain (G. S. Abdoulaev, G. Bal and A. H. Hilescher), Optics Lett., 29, 578-580, 2004. [pdf].

 

Random graphs and complex networks:

 

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

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

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

·       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 asymptotics 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.

 

Multiscale analysis and fluid dynamics:

 

·       The most intensive fluctuation in chaotic time series and relativity principle (with S-D Liu, S-K Liu and Z-T Fu), Chaos Soliton Fract., 15, 627-630, 2003.  [pdf].

·       Hierarchical similarity in an inhomogeneous turbulent wake flow behind multi-rectangular pillars (with Z. Zou et al), Acta Mechanica Sinica, 35, 519-523, 2003. [pdf].

·       Scaling equation for invariant measure (with S-K Liu, Z-T Fu and S-D Liu), Commun. Theor. Phys., 39, 295-296, 2003. [pdf].

·       Several problems in the studying of nonlinear dynamics: A review (with S-D Liu, S-K Liu, S. Liang and Z-T Fu ), Prog. Nat. Sci., 12, 1-7, 2002. [pdf].

·       The homoclinic orbit solution for functional equation (S-D Liu, Z-T Fu and S-K Liu), Commun. Theor. Phys., 38, 553-554, 2002. [pdf].

·       Multi-scaling hierarchical structure analysis on the sequence of E-coli complete genome (with J. Wang, Q. Zhang and Z-S She), Chinese Sci. Bull., 46, 1988-1992, 2001.  [pdf].

·       Scalings and structures in turbulent Couette-Taylor flow (with Z-S She, G. S. Lewis and H. L. Swinney), Phys. Rev. E, 64, 016308, 2001.  [pdf].

·       Hierarchical structure analysis of multi-scale fluctuations from highly nonlinear physical systems, Master Thesis, Peking University, Beijing, 2001. [pdf].