**• Address:** Institute of Applied Mathematics (IAM), Academy of Mathematics and Systems Science (AMSS) in the Chinese Academy of Sciences (CAS), No. 55 East Road, Zhongguancun, Beijing 100190, China.

**• Email:** xdliu@amt.ac.cn; **Phone: **86-010-82541401.

**• Born:** February, 1982, PingYao, P.R. China. Married.

### Research Areas

**• Inverse Problems for Partial Differential Equations**

◦ Inverse acoustic and electromagnetic scattering

◦ Electrical Impedance Tomography and Calderón problem

**• Applied and Numerical Analysis, Computational Mathematics**

◦ Acoustic and electromagnetic scattering theory and numerics

◦ Qualitative numerical reconstruction algorithms for inverse problems

### Education

**• PhD in Mathematics**

09/2005–07/2010

IAM, AMSS, CAS.

Thesis: Direct and Inverse Acoustic and Electromagnetic Scattering Problems

in a Layered Medium; Advisor: Prof. Bo Zhang.

**• B.Sc in Mathematics**

09/2000–07/2004

Beijing Normal University, China.

### Experience

##### Work Experience

• Professor 03/2023–present, AMSS, CAS.

• Associate Professor 04/2016–03/2023,AMSS, CAS.

• Assistant Professor 05/2012–03/2016, AMSS. CAS.

• Humboldt Postdoctor 12/2011–08/2013

KIT. Hosted by Prof. Dr. Andreas Kirsch. Supported by the Alexander von

Humboldt Foundation.

• Postdoctor 06/2010–05/2012

AMSS, CAS. Supported by the K.C.Wong Education Foundation and China

Postdoctoral Science Foundation.

##### Teaching Experience

◦ Beihang University Hua Loo-Keng Talent Program in Mathematics: Analytical Geometry, (32 hours), Sep.-Dec., 2022 and 2023 .

◦ Beihang University Hua Loo-Keng Talent Program in Mathematics: Analytical Geometry, (64 hours), Sep.-Dec., 2020 and 2021.

◦ BIT Undergraduate course: Numerical Methods, (48 hours), April.-June., 2019.

◦ CAS PhD course: Inverse Electromagnetic scattering theory, (40 hours), Sep.-Nov., 2018

◦ CAS PhD course: The mathematical theory of time harmonic Maxwell equations, (40 hours), Sep.-Nov., 2017.

◦ CAS Undergraduate course: Calculus, (40 hours), Feb.-Jul., 2017.

◦ CAS PhD course: Inverse Electromagnetic scattering theory, (60 hours), Mar-June, 2016

◦ CAS PhD course: The mathematical theory of time harmonic Maxwell

### Publications

[51] J. Li, X. Liu and Q. Shi, Uniqueness and numerical scheme for spherical shell-structured sources from the far field patterns with at most two frequencies, J.Comput. Phys., 498,2024, 112660.

[50] W. Gong, X. Liu and J. Wang, Hearing the triangles: A numerical perspective, CSIAM Trans. Appl. Math. , Vol. 5, No. 1, 2024, pp. 58-72.

[49] J. Li, X. Liu and Q. Shi, Reconstruction of multiscale elastic sources from multi-frequency sparse far field patterns, SIAM J. Appl. Math., 83(5), 2023, 1915-1934.

[48] X. Liu and Q. Shi, Identification of acoustic point sources in a two-layered medium from multi-frequency sparse far field patterns, Inverse Problems,39, 2023, 065001.

[47] X. Liu and S. Meng, A multi-frequency sampling method for the inverse source problems with sparse measurements, CSIAM Trans. Appl. Math. 4(4), 2023, 653-671.

[46] J. Li and X. Liu, Reconstruction of multiscale electromagnetic sources from multi-frequency electric far field patterns at sparse observation directions, Multiscale Model. Simul.,21(2), 2023, 753-775.

[45] F. Dou, X. Liu, S. Meng and B. Zhang, Data completion algorithms and their applications in inverse acoustic scattering with limited-aperture backscattering data, J. Comput. Phys. 469, 2022, 111550.

[44] X. Liu, S. Meng and B. Zhang, Modified sampling method with near field measurements, SIAM J. Appl. Math 82(1), 2022, 244-266.

[43] X. Ji and X. Liu, Source reconstruction with multifrequency sparse scattered fields, SIAM J. Appl. Math 81(6), 2021, 2387-2404.

[42] T. Arens, X. Ji and X. Liu, Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data, Inverse Problems 36, 2020, 105007.

[41] X. Ji and X. Liu, Identification of point like objects with multi-frequency sparse data, SIAM J. Sci. Comput 42(4), 2020, A2325-A2343.

[40] A. Alzaalig, G. Hu, X. Liu, and J. Sun, Fast acoustic source imaging using multi-frequency sparse data, Inverse Problems 36, 2020, 025009.

[39] X. Ji, Y. Jia and X. Liu, Inverse fluid-solid interaction scattering problem using phased and phaseless far field data , Acta Math Appl Sin-E 36(1), 2020, 74-94.

[38] X. Ji and X. Liu, Inverse electromagnetic source scattering problems with multi-frequency sparse phased and phaseless far field data, SIAM J. Sci. Comput 41(6), 2019, B1368õB1388.

[37] X. Ji and X. Liu, Inverse elastic scattering problems with phaseless far field data, in Special Issue in Memory of Professor Armin Lechleiter, 1982–2018, Inverse Problems 35, 2019, 114004.

[36] X. Ji, X. Liu and B. Zhang, Inverse acoustic scattering with phaseless far field data: uniqueness, phase retrieval and direct sampling methods , SIAM J. Imaging Sci., 12(2) 2019, 1163-1189.

[35] X. Ji, X. Liu and B. Zhang, Phaseless inverse source scattering problem: phase retrieval, uniqueness and direct sampling methods , J. Comput. Phys.: X 1, 2019, 100003. One of the most cited papers in the last three years.

[34] X. Ji, X. Liu and B. Zhang, Target reconstruction with a reference point scatterer using phaseless far field patterns , SIAM J. Imaging Sci., 12(1), 2019, 372-391.

[33] J. Liu, X. Liu and J. Sun, Extended sampling method for inverse elastic scattering problems using one incident wave , SIAM J. Imaging Sci., 12(1) 2019, 874-892.

[32] 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(4) 2019,

2192-2209.

[31] X. Liu and J. Sun, Data recovery in inverse scattering: from limited-aperture to full-aperture, J. Comput. Phys. 386(1), 2019, 350-364.

[30] H. Liu, X. Liu, X. Wang and Y. Wang, On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution, Inverse Problems 35, 2019, 125012.

[29] G.Hu, P.Li, X. Liu and Y. Zhao, Inverse source problems in electromagnetics, Inverse Problems and Imaging 12(6), 2018, 1411-1428.

[28] X. Ji, X. Liu and Y. Xi, Direct sampling methods for inverse elastic scattering problems, Inverse Problems 34, 035008, 2018.

[27] X. Liu, A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency , Inverse Problems 33, 085011, 2017. One of the most cited papers in 2019.

[26] H. Liu and X. Liu, Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering data , Inverse Problems 33, 065001, 2017.

[25] F. Zeng, X. Liu, J. Sun and L. Xu,(2017), Reciprocity gap method for an interior inverse scattering problem, Journal of Inverse and Illposed problems 25(1), 2017, 57-68.

[24] F. Zeng, X. Liu, J. Sun and L. Xu,(2016), The Reciprocity Gap Method for a cavity in an inhomogeneous medium, Inverse Problems and Imaging 10(3), 2016, 855-868.

[23] H. Qin and X. Liu, (2016), The linear sampling method for inhomogeneous medium and buried objects from far field measurements. Applied Numerical Mathematics, 105, 82-95.

[22] J. Li, P. Li, H. Liu and X. Liu, (2015), Recovering multiscale buried Anomalies in a two-layered medium, Inverse Problems, 31, 105006.

[21] X. Liu and B. Zhang,(2015), Recent progress on the factorization method for inverse acoustic scattering problems (in Chinese), Sci Sin Math, 45: 873-890.

[20] H. Qin and X. Liu, (2015), The interior inverse scattering problem for cavities with an artificial obstacle.

Applied Numerical Mathematics, 88, 18-30.

[19] X. Liu, (2015), The factorization method for scatterers with different physical properties, Discrete and Continuous Dynamical Systems – Series S, 8(3), 563-577.

[18] G. Hu, X. Liu, F. Qu and B. Zhang,(2015), Variational Approach to Scattering by Unbounded Rough Surfaces with Neumann and Generalized Impedance Boundary Conditions. Communications in Mathematical Sciences, 13(2), 511-537.

[17] X. Liu and J. Sun, (2014), Reconstruction of Neumann eigenvalues and support of sound hard obstacles. Inverse Problems 30, 065011.

[16] G. Hu and X. Liu, (2014) Unique Determination of Balls and Polyhedral Scatterers with A Single Point Source Wave. Inverse Problems 30, 065010.

[15] A. Kirsch and X. Liu, (2014), A modification of the factorization method for the classical acoustic inverse scattering problems, Inverse Problems 30, 035013.

[14] X. Liu, (2014), The Factorization Method for cavities, Inverse Problems 30, 015006.

[13] A. Kirsch and X. Liu, (2014), The Factorization method for inverse acoustic scattering by a penetrable anisotropic obstacle. Math. Meth. Appl. Sci. 37(8), 1159-1170.

[12] O. Bondarenko and X. Liu, (2013), The Factorization Method for inverse obstacle scattering with conductive boundary condition. Inverse Problems 29, 095021.

[11] O. Bondarenko, A. Kirsch and X. Liu, (2013), The factorization method for inverse acoustic scattering in a layered medium. Inverse Problems 29, 045010. Insight Article.

[10] A. Kirsch and X. Liu, (2013), Direct and inverse acoustic scattering by a mixed type scatterer. Inverse Problems 29, 065005.

[9] X. Liu and B. Zhang,(2012), Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. Acta Math. Sci. Ser. B Engl. Ed. 32 , 1281-1297.

[8] X. Liu and B. Zhang, (2012), Uniqueness results for inverse scattering problems. Inverse Ill-posed Probl. Ser., 56, 251-281, Walter de Gruyter, Berlin.

[7] X. Liu and B. Zhang, (2010), Direct and inverse scattering problem in a piecewise homogeneous medium. SIAM Journal on Applied Mathematics 70, 3105-3120

[6] X. Liu and B. Zhang, (2010) , Unique determination of a sound-soft ball by the modulus of a single far field datum. J. Math. Anal. Appl. 365, 619-624.

[5] X. Liu, B. Zhang and G. Hu, (2010), Uniqueness in the inverse scattering problem in a piecewise homogeneous medium. Inverse Problems 26, 015002.

[4] X. Liu, B. Zhang, (2010), A uniqueness result for inverse electromagnetic scattering problem in a two-layered medium. Inverse Problems 26, 105007.

[3] X. Liu, B. Zhang and J. Yang, (2010), The inverse electromagnetic scattering problem in a piecewise homogeneous medium. Inverse Problems 26, 125001.

[2] G. Hu, X. Liu and B. Zhang, (2009), Unique determination of a perfectly conducting ball by a finite number of electric far field data. J. Math. Anal. Appl. 352, 861-871.

[1] X. Liu and B. Zhang, (2009), A uniqueness result for the inverse electromagnetic scattering problem in a piecewise homogeneous medium. Applicable Analysis 88, 1339-1355

### Students

已指导学生

史庆祥 博士研究生 070104-应用数学

现指导学生

王静 硕士研究生 070104-应用数学

李佳磊 博士研究生 070104-应用数学

### Honors & Distinctions

• Excellent teacher. AMSS, CAS, 2021.

• Invited 45-minute speaker. The 8th International Congress of Chinese Mathematicians, June 9-14, 2019.

• Member of the Youth Innovation Promotion Association. Chinese Academy of Sciences. 2018-2021.

• Inspur Youth Academic Award. International conference on inverse problems, imaging, and applications. 2015.08.

• Chen Jingrun star of the future. AMSS, CAS, 2014.01-2016.12.

• Humboldt Research Fellowship for Postdoctoral Researchers. The Alexander von Humboldt Foundation, 2011.10-2013.08.

• Postdoctoral Work Reward Fund. K.C.Wong Education Foundation, 2011-2012.

• Postdoctoral Fellowship. China Postdoctoral Science Foundation under grant No. 20100480494, 2010.12-

2012.06.

• Excellence Award. The Presidential Award of Chinese Academy of Sciences, 2010.

• Outstanding Winner. The Presidential Award of Academy of Mathematics and Systems Science, 2009.

• Meritorious Winner. The Fifth National Post-Graduate Mathematical Contest in Modeling, 2008.