Interdisciplinary Applications

The group has a wide range of real-world applications using the above methods. These are quantum chemistry for virtual design of materials [Zas+19], paleo climate field reconstruction, medical imaging [Zas19b], two-phase flows such as in coupled gas-water systems [GZ10; ZG11; ZG13; GRZ19], plasma physics [Pfl+14], and elliptic problems [Zas15; Zas16; HZ19b] such as those arising in steady-state groundwater flows.

Quantum chemistry

Few sample molecules from a large training set for atomization energy prediction.
Selected single-fidelity models that jointly form a multi-fidelity model.

Medical imaging

Estimated mean perfusion in a simulated brain.
Probability of a given region in the brain to have low perfusion.

Paleo climate field reconstruction

(coming soon)

Fluid mechanics (e.g. two-phase flows)

Prediction of mean behavior of rising bubble in presence of uncertainties in the input.
Photorealistic visualization of two-phase flow.

Related work

  • [Zas+19] P. Zaspel et al. “Boosting Quantum Machine Learning Models with a Multilevel Combination Technique: Pople Diagrams Revisited”. In: Journal of Chemical Theory and Computation, 15(3), 2019, pp. 1546–1559.
  • [GZ10] M. Griebel and P. Zaspel. “A multi-GPU accelerated solver for the three-dimensional two-phase incompressible Navier-Stokes equations”. In: Computer Science – Research and Development, 25(1–2), 2010, pp. 65–73.
  • [ZG11] P. Zaspel and M. Griebel. “Massively Parallel Fluid Simulations on Amazon’s HPC Cloud”. In: First International Symposium on Network Cloud Computing and Applications (NCCA), 2011. 2011, pp. 73–78.
    [ZG13] P. Zaspel and M. Griebel. “Solving incompressible two-phase flows on multi-GPU clusters”. In: Computers & Fluids, 80(0), 2013, pp. 356–364.
  • [GRZ19] M. Griebel, C. Rieger, and Peter Zaspel. “Kernel-based stochastics collocation for the random two-phase Navier-Stokes equations”. In: International Journal for Uncertainty Quantification, 9(5), 2019, pp. 471–492.
  • [Pfl+14] D. Pflüger et al. “EXAHD: An Exa-scalable Two-Level Sparse Grid Approach for Higher-Dimensional Problems in Plasma Physics and Beyond”. In: Euro-Par 2014: Parallel Processing Workshops. Vol. 8806. Lecture Notes in Computer Science. Springer International Publishing, 2014, pp. 565–576.
  • [Zas15] P. Zaspel. “Parallel RBF Kernel-Based Stochastic Collocation for Large-Scale Random PDEs”. Dissertation. Institut für Numerische Simulation, Universität Bonn, 2015.
  • [Zas16] P. Zaspel. “Subspace correction methods in algebraic multi-level frames”. In: Linear Algebra and its Applications, 488, 2016, pp. 505–521.
  • [HZ19b] H. Harbrecht and P. Zaspel. “On the Algebraic Construction of Sparse Multilevel Approximations of Elliptic Tensor Product Problems”. In: Journal of Scientific Computing, 78(2), 2019, pp. 1272–1290.