Research interests


  • Nonlinear, dynamic inverse problems
  • Parameter identification in partial differential equations (PDEs)
  • Solving inverse problems without PDE solution map
  • Online parameter identification
  • Inverse problems with applications: Magnetic Particle Imaging, cell physics...
  • Learning-informed inverse problems

    • Research topics


    Magnetic Partical Imaging (MPI) [1] [2]
      MPI is a novel tracer based imaging technique invented in 2005 by Gleich and Weizenecker. This method uses a temporally-spatially varying magnetic field with field-free point to excite the nanoparticals inside a body and detect their concentration. MPI is currently in the preclinical phase exploring potential clinical applications: locate cloggings in blood vessels, locate tumors...

      Figure. Magnetization (right) of a particle in response to a dynamic external field (left); middle: initial magnetization vector [GIP]
    		TEM Example
    Parameter identification for PDEs: from neural-network-based learning to discretized inverse problems [3] [4]
      We investigate the problem of learning an unknown nonlinearity in parameter-dependent PDEs. The nonlinearity is represented via a neural network of an unknown state. The learning-informed PDE model has three unknowns: physical parameter, state and nonlinearity. We propose an all-at-once approach to the minimization problem.

      More generally, the representation via neural networks can be realized as a discretization scheme. We study convergence of Tikhonov and Landweber methods for the discretized inverse problems, and prove convergence when the discretization error approaches zero. poster
    		TEM Example