"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

  • Tanner SlagelJoseph Slagel
    Big data inverse problems
    PhD student

  • Bryan KaperickBryan Kaperick
    Randomized linear algebra
    Master Student

  • Thomas GradyThomas Grady
    GPU Randomized Iterative Methods
    Undergraduate Student

  • Arianna KrinosArianna Krinos
    Atmospheric CO2 Modeling and Estimation
    Undergraduate Student

  • Aimee MauraisAimee Maurais
    Atmospheric CO2 Modeling and Estimation
    Undergraduate Student

  • Damon ShawDamon Shaw
    Parallel Randomized Iterative Methods
    Undergraduate Student


  • Justin Krueger, Ph.D. 2017, Identifying the dynamics of small and large microbial communities.
  • Robert Torrence, M.S. 2017, Uncertainty quantification in parameter estimates of ODEs.
  • Miao Wang, Undergraduate Research, 2017, Bayesian inversion for thermal cooling experiments.
  • Olivia Ray, Master student 2016, Uncertainty quantification of greenhouse gas emission.
  • Khanh Nguyen, Undergraduate student, 2016, Least squares finite element methods.
  • Romcholo Macatula, Undergraduate student, 2016, Optimal design of experiments.

  • 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

    • Stochastic Approximations for the Solution and Uncertainty Analysis of Data-Intensive Inverse Problems, NSF DMS 1723005, PI, joint with Julianne Chung (VT); Youssef Marzouk (MIT); Luis Tenorio (Mines)
      Started in 2017
    • Virginia Tech Planning Grant: I/UCRC for Advanced Subsurface Earth Resource Models, NSF I/UCRC (1650463), PI,
      Collaborators: Colorado School of Mines
      Started 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
      Started in 2017

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

    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)