**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:**

·
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 P_{2} 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:**

·
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].