"Seht ihr den Mond dort stehen? Er ist nur halb zu sehen,
Und ist doch rund und schön! So sind wohl manche Sachen,
Die wir getrost belachen, Weil unsre Augen sie nicht sehn."
Matthias Claudius (Abendlied, um 1778)


Research summary

My research interests concern various forms of inverse problems. Driven by its application, I develop and analyze efficient numerical methods for inverse problems. Applications of interest are, but not limited to, systems biology, medical and geophysical imaging, and dynamical systems.

Challenges for solving such problems include the high dimensionality of the problem, potential ill-posedness, and constraints enforced by its application. For instance, ill-posedness of inverse problems require prior knowledge and is usually integrated as regularization. I investigate such regularization methods to obtain meaningful solutions.
With respect to the inverse problem, I develop and investigate efficient optimization methods to overcome challenges such as constraints and discontinuity.
Methods for large scale inverse problems, such as problems from imaging applications, require special considerations methods. For instance, structure or low rank approximation are investigated to solve nearby problems efficiently. To quantify uncertainty in model and estimates, I utilize Bayes and empirical Bayes frameworks.
Estimating parameter for dynamical systems (ODE constraint optimization) can be particular challenging. I investigate robust parameter estimation methods to handle even chaotic systems.


Research keywords

inverse problems, computational biology & medicine, numerical analysis, optimization, optimal experimental design, scientific computing, regularization, applied linear algebra, dynamical systems.


Research group

  • Justin Krueger Justin Krueger
    Justin Krueger's research interests lie in parameter estimation methods. In particular, he enjoys studying the limitations and computational efficiency of such methods and working to improve the methods on both fronts.
    PhD student


  • Tanner SlagelJoseph Slagel
    Big data inverse problems
    PhD student




  • Taewon ChoTaewon Cho
    Medical image processing and large scale inverse problem
    Master student




  • Robert TorrenceRobert Torrence
    Uncertainty quantification in parameter estimates of ODEs
    Master student




  • Bryan KaperickBryan Kaperick
    Randomized linear algebra
    Undergraduate student




  • Miao WangMiao Wang
    Bayesian inversion for thermal cooling experiments
    Undergraduate student




Alumni

  • Olivia Ray, Uncertainty quantification of greenhouse gas emission, Master student, 2015-2016.
  • Khanh Nguyen, Least squares finite element methods, Undergraduate student, 2016.
  • Romcholo Macatula, Optimal design of experiments, Undergraduate student, 2016.

  • Collaborators

    Julianne Chung @ Virginia Tech
    Britta Göbel @ Sanofi-Aventis
    Eldad Haber @ University of British Columbia
    Brent Johnson @ University of Rochester
    Qi Long @ Emory University
    Dianne O'Leary @ University of Maryland
    Kerstin Oltmanns @ University of Lübeck
    Mihai Pop @ University of Maryland


    Research awards

      Ongoing
    • Virginia Tech Planning Grant: I/UCRC for Advanced Subsurface Earth Resource Models, NSF I/UCRC (1650463), PI,
      Collaborators: Colorado School of Mines
      Starting in 2017
    • Quantifying Nitrogen Transformations and Loses Associated With Manure Storage to Improve Accuracy of Whole Farm Process Based Nitrogen Accounting Models, USDA NIFA: 2016-08687, Co-PI
      Collaborators: Jactone Ogejo and Biswarup Mukhopadhyay
      Starting in 2017

      Completed
    • Identifying the dynamics of small and large microbial communities, NIH R21 (1R21GM107683-01), PI
      Collaborators: Mihai Pop
      2013-2016
    • Optimal Experimental Design with Model Constraints, Texas State University Research Enhancement Grant, PI
      2011-2012
    • Energy Metabolism: Physiology and Model, Computing in Medicine and Life Sciences, Graduate School of the German Research Association (DFG), PI
      2007-2012
    • Clinical research group “The Selfish Brain”, funded by the German Research Association (DFG), I
      2005-2008
    • Research center “Plasticity and Sleep”, funded by the German Research Association (DFG), I
      2004-2005
    Lecture on Optimal Experimental Design at the IMA

    Software tools

    Optimal regularized inverse matrices (Matlab Implementation)
    Descriptive Statistics (Matlab Implementation)
    Iterative adaptive Simpson/Lobatto Method (Matlab Implementation)
    Visualization for Spherical Harmonics (Matlab Implementation)
    Continuous Shooting (Parameter Estimation for ODEs)