Hongyu Liu

Contact Information

Hongyu Liu

Department of Mathematics

City University of Hong Kong

Kowloon, Hong Kong SAR

Email: hongyu.liuip@gmail.com; hongyliu@cityu.edu.hk

Academic Experience

Professor (since 01/2020), Associate Head (since 07/2022):

Department of Mathematics, City University of Hong Kong

Acting Head and Professor (7-8/2021):

Department of Biostatistics, City University of Hong Kong

Professor (2018-20), Associate Head (2017-20), Associate Professor (2014– 18): Department of Mathematics, Hong Kong Baptist University

Assistant Professor (tenure track) (2011– 14):

Department of Mathematics, University of North Carolina, Charlotte, USA.

Lecturer/Assistant Professor (tenure track) (2011):

Department of Mathematics, University of Reading, UK.

Acting Assistant Professor (2007– 10):

Department of Mathematics, University of Washington, Seattle, USA.

Ph.D. in Mathematics (2007)  The Chinese University of Hong Kong

Research Interest

Inverse Problems and Imaging; Wave Propagations; Analysis and PDEs; Mathematical Materials Science; Scattering Theory; Spectral Theory; Geometric Integration of Dynam- ical Systems; Numerical Analysis and Scientific Computing; Bionic Learning and AIs.

Honors, Awards and Prizes

International:

World’s top 2% most highly cited scientists, List by Stanford University, 2022. Calder´on Prize, Inverse Problems International Association (IPIA), 2017.

MediaV Prize, International Conference on Inverse Problems and Related Topics, 2016, Seoul, South Korea.

Plenary Speaker, AIP Conference 2017, Inverse Problems International Association (IPIA), Hangzhou, China.

Plenary Speaker, AIP Conference 2015, Inverse Problems International Association (IPIA), Helsinki, Finland.

PIMS Postdoctoral Fellowship, Pacific Institute of Mathematical Sciences, Canada, 2008– 2010.

National/Region

Changjiang Chair Professorship, Changjiang Scholars Program, Ministry of Education, China, 2020/2021.

Minjiang Chair Professorship, Department of Education, Fujian Province, China, 2020/2021. HKMS Young Scholar Award, Hong Kong Mathematical Society, 2019.

Internal:

Faculty/School Performance Award in Scholarly Work, HKBU, 2018.

Academic Staff Fellowship, HKBU, 2017.

Award for the Best Research Output by Research Postgraduate Students, The Chinese University of Hong Kong, 2007–2008.

Scholarly:

The paper “Enhanced Near-Cloak by FSH Lining” was awarded Highly Cited Research by the Journal de Math´ematiques Pures et Appliqu´ees in 2016.

5 papers were selected into  “Editorial Highlights of the Year” by the journal,  Inverse Problems ( 2017/2015/2009/2008/2007); 1 paper was selected as “Featured Article” (2006) and 1 paper was selected as “Insight Article” (2012) by the journal, Inverse Problems.

1 paper was selected a “Research Highlight” and Cover by the journal, Journal of Mathe- matical Physics.

Research Grants and Fundings

External as PI:

PI, Hong Kong RGC General Research Fund, 11311122, 2022/2023, HK$ 690,540+HK$34,527 Mathematical study of fields concentration and gradient estimates with applications

PI, NSFC/RGC Joint Research Scheme, N CityU101/21, 2021/2022, HK$1,174,180+HK$117,418 A mathematical theory of subwavelength resonances in elasticity with applications and be-            yond

PI, Hong Kong RGC General Research Fund, 11300821, 2021/2022, HK$826,555+HK$41,328 Mathematical studies of surface- localized transmission eigenstates and applications

PI, Hong Kong RGC General Research Fund, 12301420, 2020/2021, HK$875,288+HK$43,764 Geometric properties of three classes of spectral problems with applications to inverse prob-    lems and material sciences

PI, Hong Kong RGC General Research Fund, 12302919, 2019/2020, HK$ 502,444 Mathematical and computational studies of geomagnetic anomaly detections

PI, ANR/RGC Joint Research Scheme, A CityU203/19, 2019/2020, HK$1,851,780 ALLOWAP: Algorithms for large-scale optimization of wave propagation problems

PI, Hong Kong RGC General Research Fund, 12301218, 2018/2019, HK$ 304,301

Mathematical analysis on scattering from corner singularities, inverse shape problems and geometric structures of transmission eigenfunctions

PI, Hong Kong RGC General Research Fund, 12302017, 2017/2018, HK$ 314,900 Some theoretical and numerical studies for inverse problems in wave propagations

PI, Hong Kong RGC General Research Fund, 12302415, 2015/2016, HK$ 631,972             Uniqueness, reconstruction algorithms and invisibility cloaking for inverse scattering prob- lems

PI, China NSFC Panel Grant, 11371115, 2014/2015, RMB 560,000

Mathematical research of inverse problems and invisibility cloaking in electromagnetic scat- tering

PI, USA NSF Grant, DMS 1207784, 2012/2013, US$ 105,000

Transformation optics and acoustic and electromagnetic cloaking

External as Co-I:

Co-I, China NSFC Panel Grant, 11971487, 2020/2021,  RMB 520,000

PI: DENG Youjun, Central South University.

Co-I, Hong Kong RGC General Research Fund, 405513, 2013/2014, HK$ 868,303 Mathematical analysis on determination of metrics in Maxwell’s equations

PI: ZOU Jun, The Chinese University of Hong Kong.

Played a main role in preparing the application and working on the proposed objectives.

Internal as PI:

PI, CityU Impact Grant, 2022–2024, HK$ 500,000

PI, CityU Start-up Fund, 2020, HK$ 200,000

PI, HKBU Grant, FRG1/17-18/056, 2018/2019, HK$ 50,000

PI, HKBU Grant, FRG2/16-17/071, 2017/2018, HK$ 135,000

PI, HKBU Grant, FRG1/16-17/036, 2017/2018, HK$ 50,000

PI, HKBU Grant, FRG2/15-16/012, 2016/2017, HK$ 142,500

PI, Incentive Awards for HKPFS Intakes, 2016, HK$ 100,000

PI, HKBU Grants, FRG2/14-15/033, 2014/2015, HK$ 150,000

PI, HKBU Grants, FRG1/14-15/009, 2014/2015, HK$ 50,000

PI, HKBU Start-up Fund, 2014, HK$ 120,000

PI, UNCC Start-up Fund, 2011, US$ 20,000

Professional and Outreach Activities

Secretary and Executive Committee Member, Inverse Problems International Association (IPIA), 2023–present

Panel Member of Physical Sciences, Hong Kong Research Grants Council (RGC), 2018– present

Board Member, Hong Kong Society for Industrial and Applied Mathematics, 2020–present Vice  Chair,  Activity  Group on Analysis  and  Simulation of Uncertain  Systems, China Simulation Federation, 2020–present

Secretary,  East Asia  Section of Inverse Problems International Association  (EAIPIA), 2016–present

Member, Liu Bie Ju Centre for Mathematics Sciences,  City University of Hong Kong, 2020–present

Committee Member, Preparatory Committee for the Activity Group on Inverse Problems and Imaging, China Society for Industrial and Applied Mathematics (CSIAM), 2022.       Lifetime Member, China Society for Industrial and Applied Mathematics (CSIAM).         Lifetime Member, Society for Industrial and Applied Mathematics (USA SIAM).              Selection Panel Member, Hong Kong PhD Fellowship Programme, Hong Kong Research Grants Council, 2018/19.

Selection Committee, Calder´on Prize, Inverse Problems International Association (IPIA), 2019.

Panel Member of Inverse Problems, NSF of USA, 2013.

Editorial Services:

Co-Founding Editor-in-Chief, Communications on Analysis and Computation, Amer- ican Institute of Mathematical Sciences, 2022–present.

Section Editor in Mathematics, Journal of Basic & Applied Sciences, 2022–present.

Editorial Board Members:

Journal of Nonlinear Mathematical Physics, Springer, 2022–present.  (IF: 1.163 (2021))

Heliyon, Cell Press, Advisory Board Member, Mathematics Section, 2022–present.  (IF: 3.776 (2022))

Physical Science & Biophysics Journal, 2022–present.

Mathematics, MDPI, 2021–present.  (IF: 2.592 (2021), 2.542 (5 yrs), JCR-Q1 (Mathe- matics))

Inverse  Problems  and  Imaging,  American  Institute  of Mathematical  Sciences,  2016– present. (IF:1.483 (2021), 1.462 (5 yrs), JCR-Q2 (Applied Mathematics))

Journal of Korean Society for Industrial and Applied Mathematics, 2014–present. e-Journal of Analysis and Applied Mathematics, 2018–present.

Contemporary Analysis and Applied Mathematics, 2015–2018.

Guest Editors:

East Asian Journal on Applied Mathematics, 2018.  (IF 1.660 (2021), JCR-Q2 (Applied Mathematics))

Electronic Research Archive, 2019.  (IF 1.604, JCR-Q1 (Mathematics))

AIMS Mathematics, 2022.  (IF 2.739, JCR-Q1 (Mathematics))

Patents

H. Liu and D. Ho, A  bionic  learning method for generating human  body shapes, filed for US patent, CityU Internal Ref. No.: PWG/PA/1187/2/2022.

J. Li and H. Liu, A  real-time  medical  monitoring  and  alerting  method  based  on  mobile devices  (in Chinese), filed for China Patent,  Application Number:  CN201510727435.0, Publicity Number: CN105306717A, 2016.

Research Students Supervisions

PhD Students:

Chaohua Duan (PhD 2022– , CityU)

Yuhan Li (PhD 2022– , CityU)

Li Wang (PhD 2022– , CityU)

Yueguang Hu (PhD 2021– , CityU)

Shen Zhang (PhD 2021– , CityU)

Bowen Su (PhD 2020-2021, CityU)

Hong Kong PhD Fellowship Awardee, switched his study to MSU in USA.

Youzi He (PhD 2018–2021, HKBU)

Yakun Scholarship, HKBU

Postdoctoral Scholar, The Chinese University of Hong Kong, 2021–present

Wing Yan Tsui (PhD 2017–2021, HKBU)

Dr. Wu Yee Sun Memorial Scholarship, HKBU

Lecturer, Hang Seng University of Hong Kong, 2021–present

Xinlin Cao (PhD 2016–2020, HKBU)

Hong Kong PhD Fellowship Awardee

Yakun Scholarship, HKBU

Postdoctoral Scholar, The Johann Radon Institute for Computational and Applied Math- ematics (RICAM), Austrian Academy of Sciences, 2020–2023.

Research Assistant Professor, Hong Kong Polytechnic University, 2023–present.

Shiqi Ma (PhD 2016–2019, HKBU)

Hong Kong Mathematical Society Best Thesis Award 19/20

Postdoctoral Scholar, University of Jyv¨askyl¨a, Finland, 2019–2022

Tenured Associate Professor, Jilin University, China, 2022–present

Hongjie Li (PhD 2016–2019, HKBU)

Hong Kong PhD Fellowship Awardee

Yakun Scholarship, HKBU

Hong Kong Mathematical Society Best Thesis Award 20/21

Research Assistant Professor, The Chinese University of Hong Kong, 2020–2023.     Tenure-track Assistant Professor, YMSC, Tsinghua University, China. 2023–present

Jingni Xiao (PhD 2015–2018, HKBU)

Yakun Scholarship, HKBU

Hills Assistant Professor, Rutgers University, USA, 2018–2022

Tenure-track Assistant Professor, Drexel University, USA, 2022–present

Hongpeng Sun (PhD 2013, Institute of Math, Chinese Academy of Sciences) Co-supervised with Prof. Zaijiu Shang

Tenured Associate Professor, Renmin University, China, 2016–present

Co-advised Visiting Research Students:

Yuwen Yin (Master, Changchun University of Science and Technology, China, 2020)

Xiaoxu Fei (PhD, Central South University, China, 2022)

Yan Jiang (PhD, Jilin University, China, 2022)

Yuhang Zhang (PhD, Harbin Institute of Technology, 2022)

Yan Chang (PhD, Harbin Institute of Technology, China, 2022)

Postdoctoral Mentoring:

Qingle Meng (Postdoctoral Scholar, 2022– , CityU)

PhD from Xiamen University, China

Minghui Ding (Postdoctoral Scholar, 2022– , CityU)

PhD from Hunan University

Candidate for the Hong Kong Scholars Program in the 2nd round of review

Catharine Wing Kwan Lo (Postdoctoral Scholar, 2022– , Liu Bie Jun Centre for Mathe- matical Sciences)

PhD from University of Lisbon, Portugal

Wei Wu (Research Assistant Professor, 2019–2022, HKBU)

PhD from ETH Zurich, Switzerland

Associate Professor, Jilin University, China, 2022–present

Xianchao Wang (Postdoctoral Scholar, 2019–2021, CityU)

Awardee of Postdoctoral Fellowship of the Hong Kong Scholars Program PhD from Harbin Institute of Technology, China

Associate Professor, Harbin Institute of Technology, China, 2021–present

Chun-Hsiang Tsou (Postdoctoral Scholar, HKBU, 2018–2020)

PhD from Universit´e Grenoble-Alpes, France

Assistant Professor, National Central University, Taiwan, ROC, 2021–present

Yuliang Wang (Research Assistant Professor, HKBU, 2015–2020)

PhD from Michigan State University, USA

Awardee of China Youth Talent Program

Professor, Beijing Normal University-HKBU United International College, 2020–present

Research Undergraduate Students:

Zirui Zhang, Shiyu Long, Yuqiao Zhao, CityU

2022 ICM/MCM Contest, USA, Honorable Mention

Alvin Wijaya, Andrew Wijaya Mannurung, Stephanie Wijaya, CityU

2021 CUMCM (Contemporary Undergraduate Mathematical Contest in Modelling)

Yanhao Ding, CityU

2021/2022 CityU X Sino Grand Challenges Scholars Program (approved)

Yingqiu Chen, Guo Han, Kaipeng Wang, CityU

2021 ICM/MCM Contest, USA, Meritorious Winner

Bigeng Zhang, Ziyang Wu, Houbo He, CityU

2021 ICM/MCM Contest, USA, Honorable Mention

Zizhen Song, Keli Guo, Zhongli Jiang, HKBU

2016 ICM/MCM Contest, USA, Honorable Mention

Computer Technician:

Zian Chen, CityU

IT Officer, 2022–2023

Software Development

Scholarly Work

● Book/Monograph/Book Chapter

[1]  J. Li and H. Liu,  Numerical  Methods for Inverse  Scattering  Problems, accepted for

publication by Springer and Science Press, 2023.

[2] H. Diao and H. Liu, Spectral  Geometry  and Inverse  Scattering  Theory, under review

to Springer for publication, 2022.

[3] Y. Deng and H. Liu,  Spectral  Theory  of Localized Resonances  and Applications, ac-

cepted for publication by Springer and Science Press, 2023.

[4] L. Borcea,  H. Kang,  H. Liu and  G. Uhlmann  (edited by H. Ammari and J.  Gar-

nier),  Inverse  Problems  and  Imaging, Panoramas et Syntheses, Num´ero 44,  Soci´et´e Math´ematique de France, 2015

[5]  J. Li, H. Liu and J. Zou, An efficient multilevel algorithm for inverse scattering prob-

lem,  Advances in Computation and Intelligence, Lecture Notes in Computer Science, Springer-Berlin, 2007.

● Journal Publications/Published

[1] Y.-H. Lin, H. Liu, X. Liu and S. Zhang, Simultaneous recoveries for semilinear parabolic

systems, Inverse Problems, 38 (2022), no. 11, Paper No. 115006, 39 pp.

[2] H. Liu, P. Meng, W. Shi and P. Zhang, A neural network method for time-dependent

inverse source problem with limited-aperture data, Journal of Computational and Ap- plied Mathematics, 421 (2023), Paper No. 114842.

[3]  B. Chen, Y. Gao and H. Liu, Modal approximation for time-domain elastic scattering

from metamaterial quasiparticles, Journal de Math´ematiques Pures et Appliqu´ees, 165 (2022), 148– 189.

[4]  Z. Bai,  H. Diao,  Q. Meng and H. Liu,  Stable determination of an elastic medium

scatterer by a single far-field measurement and beyond,  Calculus of Variations and Partial Differential Equations, 61 (2022), no. 5, Paper No. 170.

[5] Y.  Jiang,  H.  Liu,  J.  Zhang  and  K.  Zhang,  Boundary  localization  of transmission

eigenfunctions in spherically stratified media, Asymptotic Analysis, DOI 10.3233/ASY- 221794,

[6] X. Cao, H. Diao, H. Liu and J. Zou, Two single-measurement uniqueness results for in-

verse scattering problems within polyhedral geometries, Inverse Problems and Imaging, doi:10.3934/ipi.2022023

[7] Y. Deng, X. Fang and H. Liu, Gradient estimates for electric fields with multi-scale

inclusions in the quasi-static regime,  SIAM Multiscale Modeling & Simulation,  20 (2022), no. 2, 641–656.

[8] H. Liu, P. Meng, W. Yin and Y. Yin, The interior inverse scattering problem for a two-

layered cavity using the Bayesian method, Inverse Problems and Imaging, 16 (2022), no. 4, 673–690.

[9]  J. Li, H. Liu, L. Tang and J. Wang, Boundary homogenization of a class of obstacle

problems, Annals of Applied Mathematics, 38 (2022), no. 2, 240–260.

[10]  Z. Bai, H. Diao, H. Liu and Q. Meng,  Effective medium theory for embedded ob-

stacles in elasticity with applications to inverse problems, SIAM Journal on Applied Mathematics, 82 (2022), no. 2, 720–749.

[11] H. Liu,  On local and global structures of transmission eigenfunctions and beyond,

Journal of Inverse and Ill-posed Problems, 30 (2022), no. 2, 287–305.

[12] H. Ammari, Y. T. Chow and H. Liu, Localized sensitivity analysis at high-curvature

boundary points of reconstructing inclusions in transmission problems, SIAM Journal on Mathematical Analysis, 54 (2022), no. 2, 1543– 1592.

[13] Y. Deng, Y. Jiang, H. Liu and K. Zhang, On new surface-localized transmission eigen-

modes, Inverse Problems and Imaging, 16 (2022), no. 3, 595–611.

[14]  M. Ding, H. Liu and G. Zheng, Shape reconstructions by using plasmon resonances,

ESAIM: Mathematical Modelling Numerical Analysis, 56 (2022), no. 2, 705–726.

[15] H. Liu and  C.-H. Tsou,  Stable determination by a single measurement,  scattering

bound and regularity of transmission eigenfunction, Calculus of Variations and Partial Differential Equations, 61 (2022), no. 3, Paper No. 91.

[16] Y. Deng, H. Liu and G. Zheng, Plasmon resonances of nanorods in transverse electro-

magnetic scattering, Journal of Differential Equations, 318 (2022), 502–536.

[17] H. Li, H. Liu and J. Zou, Minnaert resonances for bubbles in soft elastic materials,

SIAM Journal on Applied Mathematics, 82 (2022), no. 1, 119– 141.

[18] Y. Deng, H. Liu, X. Wang and W. Wu, On geometrical properties of electromagnetic

transmission eigenfunctions and artificial mirage,  SIAM Journal on Applied Mathe- matics, 82 (2022), no. 1, 1–24.

[19] Y. Deng, C. Duan and H. Liu, On vanishing near corners of conductive transmission

eigenfunctions, Research in Mathematical Sciences, 9 (2022), no. 1, Paper No. 2.

[20] H. Liu, P. Meng, W. Yin and Y. Yin, On a hybrid approach for recovering multiple

obstacles, Communications in Computational Physics, 31 (2022), pp. 869–892.

[21]  G. Sun, S. Gan, Z. Shang and H. Liu, Symmetric-adjoint and symplectic-adjoint meth-

ods and their applications, Numerical Mathematics:  Theory, Methods and Applica- tions, 15 (2022), pp. 304–335.

[22]  S. Yang, Y. Liu, H. Liu and C. Wang, Numerical methods for semilinear fractional

diffusion equations with time delay, Advance in Applied Mathematics and Mechanics, 14 (2022), no. 1, 56-78.

[23] H. Diao, H. Liu and L. Wang, Further results on generalized Holmgren’s principle to

the Lam´e operator and applications,  Journal of Differential Equations, 309  (2022), 841–882.

[24] E. Bl˚asten, H. Liu and J. Xiao, On an electromagnetic problem in a corner and its

applications, Analysis & PDE, 14 (2021), no. 7, 2207–2224.

[25] Y. Gao, H. Liu, X. Wang and K. Zhang, On an artificial neural network for inverse

scattering problems, Journal of Computational Physics, 448 (2021), 110771.

[26] Y. Deng, H. Liu, X. Wang, D. Wei and L. Zhu, Simultaneous recovery of surface heat

flux and thickness of a solid structure by ultrasonic measurements, Electronic Research Archive, 29 (2021), no. 5, 3081–3096.

[27] H. Diao, H. Liu, X. Wang and K. Yang, On vanishing and localizing around corners of

electromagnetic transmission resonance, SN Partial Differential Equations and Appli- cations, 2, (2021), no. 6, Paper No. 78, 20 pp.

[28] H. Diao, H. Liu and B. Sun, On a local geometric property of the generalized elastic

transmission eigenfunctions and application, Inverse Problems, 37 (2021), 105015.

[29]  J. Lai and H. Liu, On a novel numerical scheme for the Riesz fractional partial differ-

ential equations, Mathematics, 9 (2021), 2014.

[30] Y. Deng, H. Liu and G. Zheng, Mathematical analysis of plasmon resonances for curved

nanorods, Journal de Math´ematiques Pures et Appliqu´ees, 153 (2021), 248–280.

[31] E. Bl˚asten and H. Liu, On corners scattering stably and stable shape determination

by a single far-field pattern, Indiana University Mathematics Journal, 70 (2021), no. 3, 907–947.

[32] Y.-T. Chow, Y. Deng, Y. He, H. Liu and X. Wang, Surface-localized transmission eigen-

states, super-resolution imaging and pseudo surface plasmon modes, SIAM Journal on Imaging Sciences, 14 (2021), no. 3, 946–975.

[33] E. Bl˚asten and H. Liu, Scattering by curvatures, radiationless sources, transmission

eigenfunctions and inverse scattering problems, SIAM Journal on Mathematical Anal- ysis, 53 (2021), no. 4, 3801–3837.

[34] H. Liu, C.-H. Tsou and W. Yang, On Calder´on’s inverse inclusion problem with smooth

shapes by a single partial boundary measurement, Inverse Problems, 37 (2021), 055005.

[35] H.  Diao,  H.  Liu,  L.  Zhang  and  J.  Zou,  Unique  continuation  from  a  generalized

impedance edge-corner for Maxwell’s system  and  applications to inverse problems, Inverse Problems, 37 (2021), no. 3, 035004.

[36] X. Cao, H. Diao, H. Liu and J. Zou, On novel geometric structures of Laplacian eigen- functions in R3  and applications to inverse problems, SIAM Journal on Mathematical Analysis, 53 (2021), 1263– 1294.

[37] H. Diao, X. Cao and H. Liu, On the geometric structures of transmission eigenfunctions

with a conductive boundary condition and applications,  Communications in Partial Differential Equations, 46 (2021), no. 4, 630–679.

[38]  J. Li, H. Liu and S. Ma, Determining a random Schr¨odinger operator: both potential

and source are random, Communications in Mathematical Physics, 381 (2021), 527– 556.

[39] X. Fang, Y. Deng and H. Liu, Sharp estimate of electric field from a conductive rod

and application, Studies in Applied Mathematics, 146 (2021), 279–297.

[40] H. Liu, W.-Y. Tsui,  A. Wahab and X. Wang,  Three-dimensional elastic scattering

coefficients and enhancement of the elastic near cloaking, Journal of Elasticity, 143 (2021), no. 1, 111– 146.

[41] H.  Wang,  W.  Yang,  B.  He  and  H.  Liu,  Design  and  finite  element  simulation  of

information-open  cloaking  devices,  Journal  of Computational Physics,  426  (2021), 109944.

[42] X. Cao, H. Diao and H. Liu, Determining a piecewise conductive medium body by a

single far-field measurement, CSIAM Transactions on Applied Mathematics, 1 (2020), 740-765.

[43] X.  Cao,  H. Diao,  H. Liu  and  J.  Zou,  On nodal  and singular structures of Lapla-

cian  eigenfunctions  and  applications  to  inverse  scattering  problems,   Journal  de Math´ematiques Pures et Appliqu´ees, 143 (2020), 116– 161.

[44] H. Diao, H. Liu and L. Wang, On generalized Holmgren’s principle to the Lam´e oper-

ator with applications to inverse elastic problems, Calculus of Variations and Partial Differential Equations, 59 (2020), no. 5, 179.

[45] E. Bl˚asten and H. Liu, Recovering piecewise-constant refractive indices by a single

far-field pattern, Inverse Problems, 36 (2020), 085005.

[46] H. Liu and C.-H. Tsou, Stable determination of polygonal inclusions in Calder´on’s prob-

lem by a single partial boundary measurement, Inverse Problems, 36 (2020), 085010.

[47] Y. Deng, H. Liu and W.-Y. Tsui, Identifying variations of magnetic anomalies using

geomagnetic monitoring, Discrete and Continuous Dynamical Systems, Series A , 40 (2020), no. 11, 6411–6440.

[48] Y. Deng, H. Li and H. Liu, Spectral properties of Neumann-Poincar´e operator and

anomalous localized resonance in elasticity beyond quasi-static limit, Journal of Elas- ticity, 140 (2020), 213–242.

[49] W. Yin,  W. Yang  and H. Liu,  A neural network scheme for recovering scattering

obstacles with limited phaseless far-field data, Journal of Computational Physics, 417 (2020), 109594.

[50]  D. Zhang, F. Sun, Y. Guo and H. Liu, Unique determinations in inverse scattering

problems with phaseless near-field measurements, Inverse Problems and Imaging, 14 (2020), no. 3, 569–582.

[51] E. Bl˚asten, H. Li, H. Liu and Y. Wang, Localization and geometrization in plasmon res-

onances and geometric structures of Neumann-Poincar´e eigenfunctions, ESAIM: Math- ematical Modelling and Numerical Analysis, 54 (2020), no. 3, 957–976.

[52] Y. Deng, H. Li and H. Liu, Analysis of surface polariton resonance for nanoparticles in

elastic system, SIAM Journal on Mathematical Analysis, 52 (2020), no. 2, 1786– 1805.

[53] Y. Deng, J. Li and H. Liu, On identifying magnetized anomalies using geomagnetic

monitoring within a magnetohydrodynamic model, Archive for Rational Mechanics and Analysis, 235 (2020), 691–721.

[54] X. Cao and H. Liu, Determining a fractional Helmholtz system with unknown source

and medium parameter, Communications in Mathematical Sciences, 17 (2019), no. 7, 1861– 1876.

[55] H. Liu, X. Liu, X. Wang and Y. Wang, On a novel inverse scattering scheme using res-

onant modes with enhanced imaging resolution, Inverse Problems, 35 (2019), 125012.

[56] Y. Deng, H. Li and H. Liu, On spectral properties of Neuman-Poincar´e operator and

plasmonic resonances in 3D elastostatics, Journal of Spectral Theory, 9 (2019), no. 3, 767–789

[57]  J. Li, H. Liu, W. Y. Tsui and X. Wang, An inverse scattering approach for geomet-

ric body generation:  a machine learning perspective, Mathematics in Engineering, 1 (2019), no. 4, 800–823. doi:10.3934/mine.2019.4.800.

[58]  J. Lai, H. Liu, J. Xiao and Y. Xu, The decoupling of elastic waves from a weak for-

mulation perspective, East Asian Journal on Applied Mathematics, 9 (2019), no. 2, 241–251.

[59]  J. Li, H. Liu and S. Ma, Determining a random Schr¨odinger equation with unknown

source and potential, SIAM Journal on Mathematical Analysis, 51 (2019), no. 4, 3465– 3491.

[60] H. Liu, L. Rondi and J. Xiao, Mosco convergence for H(curl) spaces, higher integrability

for Maxwell’s equations, and stability in direct and inverse EM scattering problems, Journal of the European Mathematical Society (JEMS) , 21 (2019), no. 10, 2945–2993.

[61] H. Li, S. Li, H. Liu and X. Wang, Analysis of electromagnetic scattering from plasmonic

inclusions beyond the quasi-static approximation and applications, ESAIM: Mathemat- ical Modelling and Numerical Analysis, 53 (2019), no. 4, 1351– 1371.

[62] Y. Deng, H. Liu and G. Uhlmann,  On an inverse boundary problem arising in brain

imaging, Journal of Differential Equations, 267 (2019), no. 4, 2471–2502.

[63] Y. Deng, H. Liu and X. Liu, Recovery of an embedded obstacle and the surrounding

medium for Maxwell’s system, Journal of Differential Equations, 267 (2019), no. 4, 2192–2209.

[64] X. Wang, M. Song, Y. Guo, H. Li and H. Liu, Fourier method for identifying electro-

magnetic sources with multi-frequency far-field data, Journal of Computational and Applied Mathematics, 358 (2019), 279–292.

[65] Y.  Guo,  J. Li,  H. Liu and X. Wang,  Two gesture-computing approaches by using

electromagnetic waves, Inverse Problems and Imaging, 13 (2019), 879–901.

[66]  D. Zhang, Y. Guo, J. Li and H. Liu, Locating multiple multipolar acoustic sources using

the direct sampling method,  Communications in Computational Physics, 25 (2019), no. 5, 1328– 1356.

[67] X. Cao, Y.-H. Lin and H. Liu, Simultaneously recovering potentials and embedded ob-

stacles for anisotropic fractional Schr¨odinger operators, Inverse Problems and Imaging, 13 (2019), 197–210.

[68] Y. Deng, J. Li and H. Liu, On identifying magnetized anomalies using geomagnetic

monitoring, Archive for Rational Mechanics and Analysis, 231 (2019), no. 1, 153– 187.

[69] H. Li and H. Liu, On anomalous localized resonance and plasmonic cloaking beyond

the quasistatic limit, Proceedings of the Royal Society A, 474: 20180165

[70] H.  Li,  J.  Li  and  H.  Liu,  On  novel  elastic  structures  inducing  plariton resonances

with finite frequencies and cloaking due to anomalous localized resonance, Journal de Math´ematiques Pures et Appliqu´ees, 120 (2018), 195–219.

[71]  D. Zhang, Y. Guo, J. Li and H. Liu, Retrieval of acoustic sources from multi-frequency

phaseless data, Inverse Problems, 34 (2018), 094001.

[72] H. Bastian, Y.-H. Lin and H. Liu, On localizing and concentrating electromagnetic

fields, SIAM Journal on Applied Mathematics, 78 (2018), no. 5, 2558–2574.

[73]  J. Li, H. Liu and H. Sun,   On a gesture-computing technique using electromagnetic

waves, Inverse Problems and Imaging, 12 (2018), no. 3, 677–696.

[74] X. Ji and H. Liu, On isotropic cloaking and interior transmission eigenvalue problems,

European Journal of Applied Mathematics, 29 (2018), no. 2, 253–280.

[75]  J. Li, H. Liu and H. Sun, On an inverse elastic wave imaging scheme for nearly incom-

pressible materials, IMA Journal of Applied Mathematics, 00 (2018), 1–29.

[76] H. Liu and J. Xiao, On electromagnetic scattering from a penetrable corner, SIAM

Journal on Mathematical Analysis, 49 (2017), no. 6, 5207–5241.

[77]  J. Li, X. Li, H. Liu and Y. Wang, Electromagnetic interior transmission eigenvalue

problem for inhomogeneous media containing obstacles and its applications to near cloaking, IMA Journal of Applied Mathematics, 82 (2017), 1013– 1042.

[78] E. Bl˚asten and H. Liu, On vanishing near corners of transmission eigenfunctions, Jour-

nal of Functional Analysis, 273 (2017), 3616–3632.

[79] Y. Guo, J. Li, H. Liu and X. Wang, Mathematical design of a novel input/instruction

device using a moving emitter, Inverse Problems, 33 (2017), 105009.

[80] E. Bl˚asten, X. Li, H. Liu and Y. Wang, On vanishing and localizing of transmission

eigenfunctions near singular points:  a numerical study, Inverse Problems, 33 (2017), 105001.

[81] Y. Deng, H. Liu and G. Uhlmann, On regularized full- and partial-cloaks in acoustic

scattering, Communications in Partial Differential Equations, 42 (2017), no. 6, 821– 851.

[82] H. Liu and J. Xiao, Decoupling elastic waves and its applications, Journal of Differential

Equations, 265 (2017), no. 8, 4442–4480.

[83] Y. Shi, Y. Li, S. Li and H. Liu,   State feedback design for nonlinear quadratic sys-

tems with randomly occurring actuator saturation, International Journal of Control, Automation and Systems, 15 (2017), Issue 3, pp. 1117– 1124.

[84] H. Li and H. Liu, On three-dimensional plasmon resonance in elastostatics, Annali di

Matematica Pura ed Applicata, 196 (2017), Issue 3, pp 1113– 1135.

[85] H. Liu and X. Liu,  Recovery of an embedded obstacle and its surrounding medium by

formally-determined scattering data, Inverse Problems, 33 (2017), 065001.

[86] H. Liu, Y. Wang and S. Zhong,  Nearly non-scattering electromagnetic wave set and

its application, Zeitschrift f¨ur Angewandte Mathematik und Physik, 68 (2017), 68:35.

[87]  J. Li, H. Liu and Y. Wang,  Recovering an electromagnetic obstacle by a few phaseless

backscattering measurements, Inverse Problems, 33 (2017), 035011.

[88] X. Wang, Y. Guo, D. Zhang and H. Liu, Fourier method for recovering acoustic sources

from multi-frequency far-field data, Inverse Problems, 33 (2017), 035001. (Selected into Editorial Highlights of 2017 by the journal)

[89] H. Liu, M. Petrini, L. Rondi and J. Xiao, Stable determination of sound-hard polyhe-

dral scatterers by a minimal number of scattering measurements, Journal of Differential Equations, 262 (2017), no. 3, 1631– 1670.

[90] H. Li and H. Liu, On anomalous localized resonance for the elastostatic system, SIAM

Journal on Mathematical Analysis, 48 (2016), no. 5, 3322–3344.

[91] Y. Deng, H. Liu and G. Uhlmann, Full and partial cloaking in electromagnetic scat-

tering, Archive for Rational Mechanics and Analysis, 223 (2017), 265–299.

[92] H. Liu, Y. Wang and C. Yang, Mathematical design of a novel gesture-based instruc-

tion/input device using wave detection, SIAM Journal on Imaging Sciences, 9 (2016), no. 2, 822–841.

[93]  G. Hu, J. Li, H. Liu and Q. Wang, A numerical study of complex reconstruction in

inverse elastic scattering, Communications in Computational Physics, 19 (2016), no. 5, 1265– 1286.

[94] Y. Guo, D. H¨omberg, G. Hu, J. Li and H. Liu, A time-domain sampling method for

inverse acoustic scattering problems, Journal of Computational Physics, 314 (2016), 647–660.

[95] K. Ando, H. Kang and H. Liu, Plasmon resonance with finite frequencies: a validation

of the quasi-static approximation for diametrically small inclusions, SIAM Journal on Applied Mathematics, 76 (2016), no. 2, 731–749.

[96] H. Liu and G. Uhlmann, Determining both sound speed and internal source in thermo

and photoacoustic tomography, Inverse Problems, 31 (2015), 105005. (Selected into Editorial Highlights of 2015 by the journal)

[97]  J. Li, P. Li, H. Liu and X. Liu, Recovering multiscale buried anomalies in a two-layered

medium, Inverse Problems, 31 (2015), 105006.

[98] H. Li, J. Li and H. Liu, On quasi-static cloaking due to anomalous localized resonance in R3 , SIAM Journal on Applied Mathematics, 75 (2015), 1245– 1260.

[99]  J. Li and H. Liu, Recovering a polyhedral obstacle by a few backscattering measure-

ments, Journal of Differential Equations, 259 (2015), 2101–2120.

[100]  G. Hu and H. Liu, Nearly cloaking the elastic wave fields, Journal de Math´ematiques Pures et Appliqu´ees, 104 (2015), 1045– 1074.

[101]  G. Hu, J. Li and H. Liu, Uniqueness in determining refractive indices by formally- determined far-field data, Applicable Analysis, 94 (2015), 1259– 1269.

[102]  J. Li, H. Liu, L. Rondi and G. Uhlmann, Regularized transformation-optics cloak- ing for the Helmholtz equation:from partial cloak to full cloak,  Communications in Mathematical Physics, 335 (2015), 671–712.

[103]  J. Li, H. Liu and Q. Wang, Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method, Discrete and Continuous Dynamical Systems, Series S, 8 (2015), 547–561.

[104] H. Liu, H. Zhao and C. Zou,  Determining scattering support of anisotropic acoustic mediums and obstacles,  Communications in Mathematical Sciences, 13 (2015), no. 4, 987– 1000.

[105]  J.  Li,  H.  Liu  and  H.  Sun,  Damping  mechanisms  for  regularized  transformation- acoustics  cloaking,  Contemp.  Math.,  American  Mathematical  Society,  615  (2014), 233–253. (Special issue in honor of Prof. Gunther Uhlmann’s 60th birthday)

[106]  G. Hu, J. Li, H. Liu and H. Sun, Inverse elastic scattering for multiscale rigid bodies with a single far-field pattern, SIAM Journal on Imaging Sciences, 7 (2014), 1799– 1825.

[107]  G. Hu, J. Li and H. Liu,   Recovering complex elastic scatterers by a single far-field pattern, Journal of Differential Equations, 257 (2014), 469–489.

[108]  G. Bao, H. Liu and J. Zou, Nearly cloaking the full Maxwell equations:  cloaking active contents with general conducting layers,  Journal de Math´ematiques Pures et Appliqu´ees (9), 101 (2014), 716–733.

[109]  J. Li, H. Liu, Y. Sun and Q. Wang, Ground detection by a single electromagnetic measurment, Journal of Computational Physics, 257 (2014), 554–571.

[110]  J. Li,  H. Liu and J.  Zou,  Locating multiple multiscale acoustic scatterers,  SIAM Mutliscale Modelling & Simulation, 12 (2014), 927–952.

[111]  G. Bao and H. Liu,  Nearly cloaking the electromagnetic fields,  SIAM Journal on Applied Mathematics, 74 (2014), 724–742.

[112]  J. Li, H. Liu and Q. Wang, Enhanced multilevel linear sampling methods for inverse scattering problems, Journal of Computational Physics, 257 (2014), 554–571.