Ying Liang

Phillip Griffiths Assistant Research Professor of Mathematics
Department of Mathematics
Duke University
Contact
Date Updates
October 2024 In SIAM MDS24, I will co-organize a minisymposium and present our work on neural network approaches for inverse random source problems.
October 2024 Our paper on stability for inverse random source problems of polyharmonic wave equations is available on arXiv.
October 2024 Our paper on stability for inverse random source problems of wave equations by using correlation-based data is available on arXiv.
August 2024 In Fall 2024, I will be teaching MATH 561 Numerical Linear Algebra, Optimization and Monte Carlo Simulation.
August 2024 I am excited to start a new journey in the Department of Mathematics at Duke University.
July 2024 Our paper on mathematical theory on electromagnetic diffraction is published in JMP.
June 2024 In Summer 2024, I will be teaching MA 26200 Linear Algebra and Differential Equations.
April 2024 In AMS 2024 Spring Central Sectional Meeting, I will present our work on neural network approaches for inverse random source problems.
April 2024 Our paper on stability for inverse source problems of stochastic Helmholtz equation is published in SIAP.
April 2024 Our paper on a direct probing method for the inverse problem based on the Eikonal equation is published in SISC.
March 2024 In Workshop on Recent Advances in Scientific Computing and Inverse Problems, I will present our work on theoretical and computational approaches for inverse random source problems.
January 2024 In Spring 2024, I will be teaching MA 26600 Ordinary Differential Equations.
October 2023 Our paper on data-assisted approaches for inverse random source problems is published in SIIMS.
September 2023 In Texas Tech University Applied Math Seminar, I will present our work on neural network approaches for inverse random source problems.
August 2023 In ICIAM2023, I will present our work on least-squares method for inverse medium problems.
August 2023 In Fall 2023, I will be teaching MA 30300 Differential Equations and Partial Differential Equations for Engineering and the Sciences.
June 2023 In MSML2023, I will present our work on neural network approaches for inverse random source problems.
May 2023 In LLNL DDPS Seminar, I will present our work on neural network approaches for inverse random source problems.
January 2023 In Spring 2023, I will be teaching MA 26500 Linear Algebra.
November 2022 In George Washington University Applied Math Seminar, I will present our work on neural network approaches for inverse random source problems.
October 2022 Our paper on least-squares method for inverse medium problems is published in Inverse Problems.
October 2022 In Purdue CCAM Workshop on Scientific Computing, I will present our work on neural network approaches for inverse random source problems.
September 2022 In SIAM MDS22, I will present our work on neural network approaches for inverse random source problems.
August 2022 In Fall 2022, I will be teaching MA 26600 Ordinary Differential Equations.
May 2022 In MWNAD 2022, I will present our work on least-squares method for inverse medium problems.
January 2022 In Spring 2022, I will be teaching MA 26600 Ordinary Differential Equations.
August 2021 In Fall 2022, I will be teaching MA 26600 Ordinary Differential Equations.
August 2021 I am excited to start a new journey in the Department of Mathematics at Purdue University.

Experience

Phillip Griffiths Assistant Research Professor of Mathematics
Duke University
August 2024 - Present
Durham, NC
Golomb Visiting Assistant Professor of Mathematics
Purdue University
August 2021 - July 2024
West Lafayette, IN
Research & Teaching Assistant
The Chinese University of Hong Kong
August 2016 - July 2021
Hong Kong
Teaching Assistant
Wuhan University
August 2015 - July 2016
Wuhan, Hubei

Education

PhD in Mathematics
The Chinese University of Hong Kong
Advisor: Professor Jun Zou
August 2016 - July 2021
Hong Kong
BSc in Mathematics
Wuhan University
Hongyi Honor College
August 2012 - July 2016
Wuhan, Hubei

Research

Research Interests
  • Inverse problems
  • Mathematical imaging
  • Scattering theory
  • Scientific machine learning
Publications & Preprints
  1. Peijun Li, Zhenqian Li, and Ying Liang.
    Stability for inverse random source problems of the polyharmonic wave equation.
    arXiv preprint arXiv:2410.10016.

  2. Peijun Li, Ying Liang, and Xu Wang.
    Stability estimates of inverse random source problems for the wave equations by using correlation-based data.
    arXiv preprint arXiv:2410.07938.

  3. Ying Liang and Hai Zhang.
    A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen.
    Journal of Mathematical Physics, 65 (2024), 072902.

  4. Peijun Li and Ying Liang.
    Stability for inverse source problems of the stochastic Helmholtz equation with a white noise.
    SIAM Journal on Applied Mathematics, 84 (2024), 687-709.

  5. Kazufumi Ito and Ying Liang.
    A direct probing method of an inverse problem for the Eikonal equation.
    SIAM Journal on Scientific Computing, 46 (2024), A1235-A1251.

  6. Peijun Li, Ying Liang, and Yuliang Wang.
    A data-assisted two-stage method for the inverse random source problem.
    SIAM Journal on Imaging Sciences, 16 (2023), pp. 1929-1952.

  7. Ying Liang and Jun Zou.
    Acoustic scattering and field enhancement through a single aperture.
    arXiv preprint arXiv:2011.05887.

  8. Ying Liang and Jun Zou.
    Weak Galerkin method for electrical impedance tomography.
    arXiv preprint arXiv:2011.04991.

  9. Kazufumi Ito, Ying Liang, and Jun Zou.
    Least-squares method for recovering multiple medium parameters.
    Inverse Problems, 38 (2022), 125004.

  10. Ying Liang, Hua Xiang, Shiyang Zhang, and Jun Zou.
    Preconditioners and their analyses for edge element saddle-point systems arising from time-harmonic Maxwell’s equations.
    Numerical Algorithms, 86 (2021), 281-302.

  11. Junqing Chen, Ying Liang, and Jun Zou.
    Mathematical and numerical study of a three-dimensional inverse eddy current problem.
    SIAM Journal on Applied Mathematics, 80 (2020), 1467–1492.

Presentation

Minisymposium talk
SIAM Conference on Mathematics of Data Science 2024
2024
Atlanta, GA
Invited talk
AMS 2024 Spring Central Sectional Meeting
2024
Milwaukee, WI
Invited talk
Workshop on Recent Advances in Scientific Computing and Inverse Problems
2024
Hong Kong
Invited talk
Texas Tech University Applied Math Seminar
2023
Virtual
Minisymposium talk
10th International Congress on Industrial and Applied Mathematics
2023
Tokyo
Contributed poster presentation
4th Mathematical and Scientific Machine Learning Conference
2023
Providence, RI
Invited talk
Lawrence Livermore National Laboratory DDPS Seminar
2023
Virtual
Invited talk
George Washington University Applied Math Seminar
2022
Virtual
Invited talk
Purdue CCAM Workshop on Scientific Computing
2022
West Lafayette, IN
Contributed poster presentation
SIAM Conference on Mathematics of Data Science 2022
2022
San Diego, CA
Contributed talk
Midwest Numerical Analysis Day 2022
2022
Ann Arbor, MI
Invited talk
CUHK Science Faculty Postgraduate Research Day 2020–21
2021
Hong Kong
Invited talk
5th East Asia Section of IPIA Young Scholars Symposium
2019
Beijing
Contributed poster presentation
SIAM Conference on Computational Science and Engineering 2019
2019
Spokane, WA
Invited talk
International Workshop on PDE-Constrained Optimization, Optimal Controls and Applications
2018
Sanya, Hainan
Plenary talk
Workshop on Recent Advances in PDE-based Optimal Control and Scientific Computing
2018
Wuhan, Hubei

Teaching

Instructor, Duke University (2024-Present)
MATH 563 Applied Computational Analysis
Spring 2025
MATH 561 Numerical Linear Algebra, Optimization and Monte Carlo Simulation
Fall 2024
Instructor, Purdue University (2021-2024)
MA 26200 Linear Algebra and Differential Equations
Summer 2024
MA 26600 Ordinary Differential Equations
Spring 2024
MA 30300 Differential Equations and Partial Differential Equations for Engineering and the Sciences
Fall 2023
MA 26500 Linear Algebra
Spring 2023
MA 26600 Ordinary Differential Equations
Fall 2022
MA 26600 Ordinary Differential Equations
Spring 2022
MA 26600 Ordinary Differential Equations
Fall 2021
Teaching Assistant, The Chinese University of Hong Kong (2016-2020)
MATH3230 Numerical Analysis
2019-20 Term 1
MATH3230 Numerical Analysis
2018-19 Term 1
MATH1510 Calculus for Engineers
2018-19 Term 1
MATH1010 University Mathematics
2018-19 Term 1
MATH3240 Numerical Methods for Differential Equations
2017-18 Term 2
MATH3230 Numerical Analysis
2017-18 Term 1
MATH3240 Numerical Methods for Differential Equations
2016-17 Term 2
MATH3230 Numerical Analysis
2016-17 Term 1
Teaching Assistant, Wuhan University (2015-2016)
Calculus for Engineers
2015-16 Term 1