Guozhi Dong

Affiliations: (1) Institute for Mathematics, Humboldt-Universität zu Berlin
(2) Weierstrass Institute for Applied Analysis and Stochastics


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Welcome to my homepage. I am a postdoctoral researcher at the Humboldt University of Berlin and Weierstrass Institute in Berlin, working in the group of Professor Michael Hintermüller. I am also a member of the Berlin Mathematics Research Center, which is one of the Germany Clusters of Excellence.
Research experience
I have working experience in a few tightly connected areas in applied and computational mathematics: Inverse and imaging problems, their variational regularization methods, with connections to some geometric partial differential equations; Optimal control of partial differential equations; Numerical solutions of (partial) differential equations, particularly for solutions and data on manifolds; Mathematics of deep learning and their applications.
I always feel a lot of fun from sports, including many kinds of ball games, range from tiny, e.g., table tennis, to large, e.g., basketball, but not limitted to these. For instance, swiming, playing chess/cards, jogging, skating, music are also my hobbies. I like literature, poem. Sometimes, I write poems, but the frequency becomes less and less. I could have become a writer or a poet if I did not choose to be a mathematician. When I have time, I enjoy cooking for my family and friends as well.
Before joining Berlin, I was a research asistant at the Computational Science Center, University of Vienna, where I completed my PhD degree (with distinction) under the supervision of Professor Otmar Scherzer. Earlier than that, I have been working as an assistant (secretary) on scientific affairs in the Faculty of Mathematics and Computer Sciences at Hunan Normal University, Changsha, China, where I finished both my Bachelor degree and Master degree.

2017– now Postdoctoral researcher,Humboldt University and Weierstrass Institute, Berlin, Germany
2012–2017PhD candidate in Mathematics, University of Vienna, Vienna, Austria
2010–2011 Erasmus Mundus Master student, University of Eastern Finland, Kuopio Campus, Kuopio, Finland
2009–2012 Master study in Computational Mathematics (part time), Hunan Normal University, Changsha, China
2007–2012Secretary of scientific affairs in the Faculty of Math & Computer Sciences, Hunan Normal University, Changsha, China
2003–2007Undergraduate majored in Informatics and Computational Sciences, Hunan Normal University, Changsha, China
Selected Publications
  1. Discontinuous Galerkin methods for Laplace-Beltrami operator on point clouds [pdf]
    with Hailong Guo and Zuoqiang Shi, in review (2021).
  2. Optimization with learning-informed differential equation constraints and its applications [pdf]
    with Michael Hintermüller and Kostas Papafitsoros, in review (2021).
  3. Superconvergence of differential structure on manifolds and its applications [pdf]
    with Hailong Guo, in review (2021).
  4. Convergence Rates of First and Second Order Dynamics for Solving Linear Ill-posed Problems [pdf]
    with Radu I. Bot, Peter Elbau and Otmar Scherzer, Foundations of Computational Mathematics, 2021.
  5. A Class of Second Order Geometric Quasilinear Hyperbolic PDEs and Their Applications in Imaging [pdf]
    with Michael Hintermüller and Ye Zhang, SIAM Journal on Imaging Sciences, 14(2), 645-688, 2021.
  6. Quantitative Magnetic Resonance Imaging: From fingerprinting to integrated physics-based model [pdf]
    with Michael Hintermüller and Kostas Papafitsoros, SIAM Journal on Imaging Sciences, 12(2), 927-971, 2019.
  7. Parametric Polynomial Preserving Recovery on Manifolds [pdf]
    with Hailong Guo, SIAM Journal on Scientific Computing, 42 (3), A1885-A1912, 2020.
  8. Nonlinear Flows for Displacement Correction and Applications in Tomography [pdf]
    with Otmar Scherzer, SSVM'17 Proceedings, Lecture Notes in Computer Sciences, in F. Lauze et al. editors, volume 10302, 283-294, 2017. Springer International Publishing.
  9. Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces [pdf]
    with Bert Juttler, Otmar Scherzer and Thomas Takacs, Inverse Problems and Imaing, 11(2), 221-246, 2017.
  10. Infnite Dimensional Optimization Models and PDEs for Dejittering [pdf]
    with Aniello R. Patrone, Otmar Scherzer, and Ozan \"Oktem, SSVM'15 Proceedings, Lecture Notes in Computer Sciences, in Aujol, J., Nikolova, M., Papadakis, N. editors, volume 9087, p678-689, 2015. Springer-Verlag.
  11. Efficiency Analysis of European Freight Villages-Three Peers for Benchmarking [pdf]
    with Congcong Yang and Alfred Taudes, Central European J. Operation Research, 25(1), 91-122, 2017
  12. Scale and Edge detection with Topological Derivatives [pdf]
    with Markus Grasmair, Sung Ha Kang and Otmar Scherzer, SSVM'13 Proceedings, Lecture Notes in Computer Sciences, in A. Kuijper et. al editors, volume 7893, p404-415, Berlin, Heidelberg, 2013. Springer-Verlag.
Selected Talks and Presentations
– August 2021 A IMA Workshop on Mathematical Foundation and Applications of Deep Learning, Purdue University (online format), USA.
– March 2021 91^{st} GAMM Annual Meeting 2021, Section Mathematical signal and image processing, Kassel (online format), Germany.
– January 2020 Tsinghua Sanya International Mathematical Forum: Workshop on Efficient Algorithms in Data Science, Learning and Computational Physics, Sanya, China.
– August 2019 ICCOPT 2019, the 6th International Conference on Continuous Optimization, contributed section: Big Data and Machine Learning, Berlin, Germany.
– April 2019 The Mathematics of Imaging, Institute of Henri Poincare trimester, Paris, France.
– January 2019 Winter-school: the mathematics of deep learning, Centre International de Rencontres Math\'ematiques (CIRM), Marseille, France.
– June 2018 SIAM Imaging Conference 2018 Mini-symposium: Learning and adaptive approaches in image processing, Bologna, Italy.
– June 2017 SSVM 2017, 6th International Conference on Scale Space and Variational Methods in Computer Vision, Kolding, Denmark.
– May 2017 AIP 2017 Mini-symposium: Some Recent Advances in Regularization Theory and Numerical Algorithms for ill-posed Inverse Problems, Hangzhou, China.
– April 2016 Training School on Algebraic Reconstruction Methods in Tomography, Technical University of Denmark, Copenhagen, Denmark.
– August 2015 ICIAM 2015 Mini-symposium: Regularization Methods for Biomedical Image Analysis on Manifolds, Beijing, China.
– August 2015 ICIAM 2015 Mini-symposium: Iso-geometric Analysis: Design-through-analysis tools in CAD/CAE, Beijing, China.
– June 2015 SSVM 2015, 5th International Conference on Scale Space and Variational Methods in Computer Vision, Bourdeaux, France.
– April 2014 Isogeometric Analysis and Applications 2014, Annweiler, Germany.
– June 2013 SSVM 2013, 4th International Conference on Scale Space and Variational Methods in Computer Vision, Graz, Austria.