Dr. Raphael Kruse

Head of junior research group 'Uncertainty Quantification'

Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
+49 (0) 30 314 23354
kruse@math.tu-berlin.de
Website


Research focus

Numerics for stochastic and rough differential equations
Monte Carlo methods

Projects as a project leader

  • SE21

    Data Assimilation for Port-Hamiltonian Power Network Models

    Dr. Raphael Kruse / Prof. Dr. Volker Mehrmann / Dr. Matthias Voigt

    Project heads: Dr. Raphael Kruse / Prof. Dr. Volker Mehrmann / Dr. Matthias Voigt
    Project members: Riccardo Morandin
    Duration: -
    Status: running
    Located at: Technische Universität Berlin

    Description

    In this project we will study the modeling of power networks by employing the port-Hamiltonian framework. Energy based modeling with port-Hamiltonian descriptor systems has many advantages, e. g., it accounts for the physical interpretation of its variables, it is best suited for the modular structure of the network, since coupled port-Hamiltonian systems form again a port-Hamiltonian system and it encodes these properties in algebraic and geometric properties that simplify Galerkin type model reduction, stability analysis, and also efficient discretization techniques. To improve the predictions that one obtains from such models we suggest to employ data assimilation and state estimation techniques by incorporating the measurement data. These would allow to take the uncertainty in the measurements and the presence of unmodeled dynamics as well as data and modeling errors into account. The improved predictions can then be used to control the network such that (the expected value of) the load is kept as constant as possible. To control the network we propose to use techniques of model predictive control (MPC) which solve a sequence of finite horizon optimal control problems. The method uses predictions of the state and computes a local optimal control which is then used for the model simulation in the next iteration. This framework is very flexible, since it allows control in real time and the incorporation of nonlinear dynamics and/or inequality constraints. It has already been used successfully within other areas of energy network control. Our new ansatz will also incorporate the stochastic effects into the model predictive control framework using data assimilation. Our vision is to develop numerical methods for network operators that allows the incorporation of model uncertainities for improving simulation and control of power networks.

    http://www3.math.tu-berlin.de/numerik/NumMat/ECMath/SE21/
  • CH-TU25

    Weak convergence of numerical methods for stochastic partial differential equations with applications to neurosciences

    Dr. Raphael Kruse

    Project heads: Dr. Raphael Kruse
    Project members: -
    Duration: 01.05.2014 - 30.04.2020
    Status: running
    Located at: Technische Universität Berlin

    Description

    In this project we develop and investigate novel numerical methods for the discretization of stochastic partial differential equations arising, for instance, in neuroscience. Our numerical methods are based on the Galerkin finite element method combined with suitable time stepping schemes such as the backward Euler method or backward difference formulas.

    http://www.math.tu-berlin.de/fachgebiete_ag_modnumdiff/diffeqs/v_menue/fg_differentialgleichungen/nwg_uq0/v_menue/research_projects/weak_convergence_of_numerical_methods_for_spdes_with_applications_to_neurosciences/