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Data-Driven Inversion and Learning:

·         Instance-Wise Adaptive Sampling for Dataset Construction in Approximating Inverse Problem Solutions (with J. Han and N. Soedjak), Submitted, 2025. [pdf].

·         A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems (with L. Zhang), J. Comput. Phys., 114232, 2025. [pdf].

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

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

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

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

·         A generalized weighted optimization method for computational learning and inversion (with B. Engquist and Y. Yang), ICLR, 2022. [pdf].

·         Coupling deep learning with full waveform inversion (with W. Ding and Lu. Zhang), Handbook of Numerical Analysis, 27, 2026. [pdf].

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

Inverse Problems for Mean-Field Game Models:

·        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]

·         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]

Phase Retrieval in Nonlinear Optics:

·         Phase retrieval via media diversity (with Y. Cheng and N. Soedjak), Inverse Problems, 41, 075009, 2025. [pdf]

·         Chosen-plaintext attacks of double random phase encryption with nonlinear optical media (with Y. Cheng, Y. Chen, and N. Soedjak), 2025. [pdf]

Numerical Analysis and Scientific Computing:

·         A discontinuous Galerkin method for one-dimensional nonlocal wave problems (with Q. Du, L. Zhang, and Y. Zhou), Submitted, 2025. [pdf].

·         Error analysis for the implicit boundary integral method (with Y. Zhong, O. Runborg, and R. Tsai), BIT Numer. Math., 65, 8, 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, K. Otness, and D. Rim), Submitted, 2024. [pdf]

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

Hybrid Multi-Physics Inverse Problems:

·         Forward and inverse problems of a semilinear transport equation (with Y. Zhong), Submitted, 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]

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

·         Unique determination of absorption coefficients in a semilinear transport equation (with Y. Zhong), SIAM J. Math. Anal., 53: 5158-5184, 2021. [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 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), SIAM J. Appl. Math., 83, 1677-1695, 2023. [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].

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].

Miscellaneous Topics:

·         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].